Valuing New Economy Companies
using Real Options Theory with Visualization
by
Arturo Manuel Rodriguez Ramirez
B.S. Electrical Science and Engineering 1999
B.S. Management Science 2000
Massachusetts Institute of Technology
Submitted to the Department of Electrical Engineering and Computer Science in partial
fulfillment of the requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science
at the
MASSACHUSETTS INSTITUTE
Massachusetts Institute of Technology
February 20013
©2001 Arturo Manuel Rodriguez Ramirez
All Rights Reserved
OF TECHNtOLOGY
1 2002
LIBRARIES
The author hereby grants to MIT permission to reproduce and to distribute publicly paper
and electronic copies of this thesis and to grant others the right to do so.
Signature of Author:
Arturo Manuel Rodriguez Ramirez
Department of Electrical Engineering and Computer Science
February 6, 2001
Certified by:
S. P. Kothari, Thesis Supervisor
Gordon Y. Billiard Professor of Accounting and Finance
M )Alfred P. Sloan School of anagement
Accepted by:
iommittee on Graduate Theses
Arthur C. Smith, Chairman,
Department of Electrical Engineering and Computer Science
BARKER
Valuing New Economy Companies
using Real Options Theory with Visualization
by
Arturo Manuel Rodriguez Ramirez
Submitted to the Department of Electrical Engineering and Computer Science on
February 6, 2000 in partial fulfillment of the requirements for the Degree of Master of
Engineering in Electrical Engineering and Computer Science
ABSTRACT
This paper concerns the valuation of new economy companies using real options models
and ideas. Real options theory determines the value of any economic activity where
uncertainty and flexibility are present, and where another activity with the exactly same
payoff as the former can be valued. New economy companies are portfolios of uncertain
projects combined with some certain cash flow streams. This uncertainty explains their
volatility, rates of growth and high multiples as normal parts of their development. It also
explains market bubbles and crashes and other economic events in the same terms. In the
real options framework expenditures in capital equipment and some intangibles -such as
R&D, and strong sales and marketing organizations- are really investments in growth. To
make the study of real options more intuitive and informative we use and endorse the use
of visual representations in the form of diagrams and graphs.
Thesis Supervisor: S. P. Kothari
Title: Gordon Y. Billard Professor of Accounting and Finance
1-2
Acknowledgements
I would like to thank Professor S. P. Kothari for his endorsement of my original
idea, his invaluable guidance in channeling this idea into a concrete, useful and current
topic, and his unwavering patience through my study and development of the project. His
contribution to this work began more than a year ago, when he taught me the fundaments
of financial valuation and inspired me to pursue this line of study further, and continued
all the way to the culmination of this paper.
I would also like to thank Professor Erich P. Ippen for supporting me during my
years at MIT. I certainly believe that without his understanding and character it would
have been harder for me to make it to the end. I also would like to thank every professor,
TA and administrator with whom I ever dealt with while at MIT, especially those that
appreciated me and lent me his or her support.
Finally I would like to thank all my family and friends, who whether abroad or at
MIT have lent me their support and made it possible for me to find the strength and
happiness necessary to have made it all possible.
1-3
Table of Contents
Introduction: The New Economy......................................................................
Literature Review ..............................................................................................
Option Pricing Theory ...............................................................................
2.1
2.2
Real Options Theory and Applications .....................................................
3
Real Options Review.........................................................................................3-13
2
1-6
2-8
2-8
2-8
Uncertainty, Flexibility and the Law of One Price .................................. 3-13
3.1
3-15
Option Fundamentals ...............................................................................
3.2
3-16
3.2.1
European versus American Options .....................................................
3.2.2
Call and Put Options............................................................................3-16
3-17
3.2.3
Long and Short Option Positions .........................................................
3.2.4
Option Payoff Diagrams......................................................................3-17
Option Portfolios and Fractional Options.............................................3-18
3.2.5
Put-Call Parity.....................................................................................3-20
3.2.6
3-21
Option Pricing Theory ..............................................................................
3.3
The Binomial and other Decision Tree Option Pricing Methods .......... 3-21
3.3.1
3.3.1.1
The Event Tree................................................................................3-21
3-23
3.3.1.2
The Decision Tree ...........................................................................
Portfolio Replication........................................................................3-24
3.3.1.3
3-25
3.3.1.4 The Binomial Probability Formulas .................................................
3.3.2
The Black-Scholes Method..................................................................3-26
3.3.2.1
3.3.2.2
3.3.2.3
3.3.2.4
3.3.2.5
3.3.2.6
3.4
Types
3.4.1
Risk free interest rate "r".................................................................3-28
Value lost over duration of option "6" ............................................. 3-28
Time to expiry "T"............................................................................3-29
3-30
Volatility of expected cash flows "a"..............................................
3-31
Present value of fixed costs "K" ......................................................
Present value of expected cash flows "5".........................................3-32
of Options by Structure and Application ...................................... 3-32
Single Option ......................................................................................
3-33
3.4.1.1
Growth, Deferral Expansion, and Extension Options ....................... 3-33
3.4.1.2
Exit -or Abandonment-, Contraction, and Shortening Options.........3-35
Rainbow Options.................................................................................3-36
3.4.2
3-37
3.4.3
Compound Options/Learning Options .................................................
3-39
Same-Project Option Portfolios ...........................................................
3.4.4
4
Valuinig Projects and Companies using Real Options.....................................4-40
4.1
Understanding New Economy Com panies...............................................4-41
W hat we mean by New Economy Companies......................................4-41
4.1.1
Projects and Project Portfolios.............................................................4-43
4.1.2
4.1.3
Project Life-Cycle and Portfolio Analysis............................................4-45
Understand the Company: W hat does it do?...........................................4-47
4.2
4.2.1
W hat lines of businesses is it engaged in 9 ........................ . . . . . . . . . . . . . . . . . . . .4-48
4.2.2
How did it get there?........................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-48
4.2.3
Where does is it intend to go?................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-49
W hat does/did the path depend on?............................. . . . . . . . . . . . . . . . . . . . . . . . . . 4-50
4.2.4
4.2.5
W hen do/did those events happen?............................. . . . . . . . . . . . . . . . . . . . . . . . . .4-51
1-4
4.2.6
Sketch an evolutionary tree for the company........................................4-51
4.3
Structure the Problem...............................................................................4-53
Model the Uncertainty: Draw an Event Tree........................................4-53
4.3.1
4.3.2
Model Managerial Flexibility: Draw a Decision Tree .......................... 4-55
4-56
4.3.3
Estimating the Real Options Payoff .....................................................
4.3.3.1
How to Account Depreciation, Amortization and Depletion.............4-57
4.3.3.2 How to Account Operating Expenses...............................................4-57
Compute and Understand the Real Option Value ................................. 4-59
4.3.4
4-63
4.4
Sum the Values and Analyze the Compan .............................................
Review and Redesign if Necessary............................................................4-64
4.5
4.5.1
Compare the Real Options Value with a DCF One .............................. 4-64
Compare the Computed Values with the Market Capitalization ........... 4-64
4.5.2
In Case of Discrepancies Look at the Following .................................. 4-65
4.5.3
4.5.3.1
Check for double and under accounting. .......................................... 4-66
4.5.3.2
Has any project been overlooked or confused?.................. . . . . . . . . . . . . . . . 4-66
4.5.3.3
Are the DCF projections and WACC reasonable?............... . . . . . . . . . . . . . 4-67
4.5.3.4
Are the option payoffs and asset value accurate?................
. ..... ........
4.5.4
Redesign if necessary but remember the 80/20 rule .............................
Two Examples of Valuing Internet Infrastructure Companies ......................
5
5.1
Sycamore Networks ..................................................................................
5.1.1
Understanding the Optical Networks Company ...................................
Structuring its Product Portfolio ..........................................................
5.1.2
5.1.2.1
The SN 6000 ...................................................................................
5.1.2.2
The SN 8000 ...................................................................................
4-68
4-69
5-70
5-70
5-70
5-72
5-72
5-72
5-72
S ILV X .............................................................................................
5 .1.2 .3
5-72
5.1.2.4
SN 16000 ........................................................................................
5.1.3
Understanding where its value comes from..........................................5-73
5-75
5.1.4
R eview ing the M odel ..........................................................................
Check Point Software Technolo2ies Inc...................................................5-76
5.2
5.2.1
Understanding the Security Software Company ................................... 5-76
5-78
5.2.2
Structuring its Product Portfolio ..........................................................
5 .2 .2 .1
S ecurity ...........................................................................................
5-7 8
6
5-78
5.2.2.2
Virtual Private Networks .................................................................
5-78
Network Performance and Availability ............................................
5.2.2.3
5-78
Network Management .....................................................................
5.2.2.4
5.2.3
Understanding where its value comes from..........................................5-79
5-81
5.2.4
Reviewing the Model ..........................................................................
6-83
Conclusion and a Look into the Future ...........................................................
7
Appendices ........................................................................................................
7-85
8
References .........................................................................................................
8-86
1-5
1
Introduction: The New Economy
To understand the motivation for this paper it helps to set ourselves in the context
of contemporary market history. At the time of this writing it is January 2001, and in the
past two years new economy companies have experienced their two most extreme equity
price performances ever. 1999 saw the heavily new economy weighted Nasdaq
Composite Index appreciate by more than 80%, peaking at a little above 5000 in March
2000, only to retreat in 2000 by more than 40%, bottoming at a little under 2300 in
January 2001. In individual issues some large and many smaller technology names
gained hundreds of percent returns in 1999 -these include Qualcomm, Oracle and many
Internet companies- only to see their value fall down precipitously the following year.
Many Internet high fliers, including the most profitable companies, lost 80% or even 90%
of their market value from their highs. Yahoo!, a company that had risen steadily since
IPO by hundreds of percent per year and the leading web media property fell from a high
of about $250 a share to the 30s today: an 88% drop. Similar examples can be found in
Inktomi, Ebay, Amazon.com, and others all down more than 80% from their March 2000
highs. Even established PC industry companies such as Microsoft, Intel and Dell, all fell
more than 50% from their highs. Did the conditions of the world change so quickly in a
matter of months? Where the 1999 prices or the 2000 ones the correct values of these
companies? What are the true values of these new economy companies?
One of the reason this has been such a difficult question to answer is that these
companies thrive under conditions of great uncertainty. They are companies that grow
very fast their top and bottom lines, that have unsettled technological issues that get
resolved by the day, that ship products in markets with not yet clearly defined standards
and where competition is intense, and that they generally develop under conditions where
they can make or break billions of dollars in revenues and earnings in the matter of just a
few years. In short they must grow in a high competition environment where flexibility
and adaptability is the key to survival and success. Management and technology plans
can not be done for more than two years ahead, and product cycles last not much more
than a year.
Under these conditions traditional ideas of management and valuation break
down. The companies' management must learn to take real time decisions to thrive; and
1-6
thus they can not by any means guarantee courses of action based on uncertain future
events. Put together the unpredictability of their product and service markets with that of
the companies' management, and valuators and investors suddenly face the hapless task
of pricing companies whose future you can not see in one year time, with tools that have
been designed assuming it is known what companies will be doing in five years time.
This is the dilemma valuators and the financial markets face when trying to apply
discounted cash flow methods to the new economy. The result is volatile markets.
What we need is a theory that allows us to price uncertainty and flexibility. This
theory exists and was developed for financial options by Fisher Black, Myron Scholes,
and Robert Merton in the 70s, and later extended to the world of real projects beginning
with the work of Stewart Myers. It is option pricing theory. Real options pricing theory is
used to value uncertain projects and some companies today. What we need is to further
systematize the process of valuing entire companies. Some of these companies -for
example startups- will be straightforward to value using real option project techniques
since they are in essence single project companies. Larger more mature and diversified
companies will be more complex and will require a more flexible approach. We intend to
discuss various issues relevant to this process.
In particular we intend to focus on understanding where is value coming from and
how can it be estimated without too much need for mathematical sophistication. We
intend to explain and define what truly is a new economy company, we intend to
understand these companies in a light that combines valuation with strategy, and we
intend to help our understanding by diagrams and graphs that condense and visualize the
relevant information. But from this what we hope to transmit most is that beyond its
value for equity pricing real options theory is a most powerful mental model for both
understanding value and implementing strategy.
Some great investors -like Warren Buffett- have shied away from new economy
companies because they feel uncomfortable predicting where they will be in any amount
of time. What we hope with this paper is to contribute to tackling this problem so that not
only stock pickers, but investors and entrepreneurs of all sorts, will start thinking of
uncertainty and flexibility like their allies from which they can profit even more than they
can loose.
1-7
2 Literature Review
2.1 Option Pricing Theory
The development of real option theory would not have been possible had option
pricing theory not been given a start by Fisher Black and Myron Scholes together with
Robert Merton in their seminal 1973 papers "The pricing of options and corporate
liabilities" (1) and "Theory of rational option pricing"
(2).
In the papers they show that the
relationship between the price of stock and the option on it is a partial differential
equation subject to boundary conditions whose close-form solution in the case of a single
contingent variable and expiry date is the Black-Scholes equation. An important
requirement for the correct solution is that the law of one price holds. That is equivalent
to saying that there should be no arbitrage opportunities.
John Cox and Stephen Ross, later together with Mark Rubinstein, developed the
binomial option-pricing model. In their papers "The valuation of options for alternative
stochastic processes"
(3) and
"Option pricing: a simplified approach"
(4)
they introduce
the idea that option prices should be unique and independent from each investor's risk
preference. They also develop an amenable alternate way of computing option prices that
is usable in a wide range of applications and will be the foundation of our work in this
paper.
Many other important contributions to option pricing theory have been made, but
we will focus on those of greater relevance to real options here. For general books on the
subject of option pricing theory Cox and Rubinstein's own Options Markets
(5)
is
considered among the best available. Another good text is John C. Hull's Options,
Futures and other Derivatives (6).
2.2 Real Options Theory and Applications
Stewart Myers was the first to coin the term "real options". In his seminal 1984
paper "Finance Theory and Financial Strategy"
(7) he
discussed the issues dividing the
two branches of management science and the inconsistencies that must be resolved before
they can be united. He argues that the inadequacy and misuse of the Net Present Value
(NPV) model coupled with financial theorists and strategists' lack of a common theory of
firm value is at the root of the problem. Myers correctly points out many of the faults of
2-8
NPV in valuing projects that provide no immediate cash returns but that nevertheless
strategists agree are of great value to the firm. Among them the misuse of NPV itself
accounts for much of the error but he nevertheless explains that even if perfectly well
implemented NPV would still fail to capture "the links between today's investments and
tomorrows opportunities". Because of that he concludes the paper calling for the
development of a unifying theory of value that could be used across both fields:
"Strategic Planning needs finance. Present value calculations are needed as a check on
strategic analysis and vice versa. However, standard discounted cash flow techniques will
tend to understate the option value attached to growing profitable lines of business.
Corporate finance theory requires extension to deal with real options."
At around the same time W. Carl Kester published "Today's options for
tomorrow's growth" (8). In it he adds to Myers' argument by expanding the ideas behind
real options theory. He uses an example were NPV thinking lead management to the
wrong decision, which would have been prevented if they had analyzed the problem
using options pricing theory instead. He explains that various factors -including increased
project cash flow volatility, increased interest rates, and increased length of time that the
project can be deferred- add to project value. This is in contradiction to NPV arguments
but is the natural outcome of options thinking. He also points out that real options can be
either proprietary to the firm or shared with competitors thus giving birth to strategic
growth options theory. He further distinguishes between many other important types of
options such as simple and compound, and expiring and non-expiring. And most
important he argues that options valuation is in the interest of the firms shareholders at all
time horizons: "Because investment decisions today can create the basis for investment
decisions tomorrow, capital allocations made in any year are vital steps in the ultimate
achievement of strategic objectives. By the same token, a long-range plan necessarily
implies the cultivation of particular investment opportunities and can have a direct,
dollars and cents impact on a company's stock price in the near term as well".
In "Valuing Managerial Flexibility" (9)
Lenos Trigeorgis and Scott Mason
provide one of the early papers on how to apply real options theory from a practical point
of view. They also defend real options theory from decision tree analysts' by showing
that real options theory incorporates the market opportunity to trade and borrow and
2-9
therefore is more economically correct. They once again argue that managerial flexibility
is an element not present in NPV calculations and that the resulting payoff asymmetry
can not be successfully captured by NPV techniques. They introduce the use of decision
trees in analyzing the future payoffs of contingent projects but argue against going all the
way with decision tree analysis because of the difficulties of determining the right
discount rate. Instead they use the fundamental option principle of project payoff
replication through the use of a twin security and risk less bond. They provide examples
of how to compute the values of various types of real options, including those to defer
investment, expand or contract.
In one of the more recent papers (1995) on real options theory "The Options
Approach to Capital Investment" (10) Avinash Dixit and Robert Pindyck set out to
explain several of the faulty assumptions of NPV and how real options theory addresses
this issues. In particular they point to the fact that NPV assumes investment decisions are
reversible and can not be deferred, while in many cases neither of these assumptions
holds true. They argue that often it is valuable for a company to create options for itself in
order to potentially capture value in the future, and that often it is worthy to delay
exercising the option until all the necessary information is available. As examples they
explain that options thinking proves that it may be more profitable for ongoing
companies that are loosing money to continue operations -contrary to NPV thinking- by
showing that incurred costs are already sunk and that they give the company rights to
earn future profits as long as the productive assets are not sold off. Furthermore they
argue that financial markets value more highly investments that create options -such as
the new economy startups- than those that exercise them. Also they argue that many
options underlying assets are intangibles, such as know-how and brand, as well as the
more obvious assets of production facilities or resources.
In his 1996 paper "Applying 'Options Thinking' to R&D Valuation" (")Terrence
Faulkner argues that the ideas of real options theory must be used to value knowledge
creating projects and to think about strategy. In particular Faulkner emphasizes that even
decision tree analyses that are based on option ideas are an acceptable way of computing
'option thinking' values. This method involves assigning probabilities to uncertain events
and computing the expectation of the outcomes and their respective contingent decisions.
2-10
But more significantly this method leads managers to think strategically in terms of
flexibility, phased investments, long-term focus, and the value of intangibles. Faulkner is
careful to point out however that options thinking can also be misused to casually justify
unprofitable projects.
A good introduction to the uses of real options thinking in corporate strategy is
Leslie and Michael's (1997) paper "The Real Power of Real Options"
(12).
The authors
set out to market the idea of real options as a strategic tool for managers engaged in
capital expenditure decisions where there is uncertainty in the future payoff. Their
exposition is centered on the analogy of real and financial options, and as such they
explain the Black-Scholes option pricing formula as applied to real options. They explain
the meaning of the six parameters of Black-Scholes in real options, and the strategic
measures that management can take in manipulating these parameters to maximize option
value. Finally they go over two examples in the UK energy sector where the companies
realized substantial shareholder value through the use of real options thinking.
Timothy Luehrman's "Investment Opportunities as Real Options: Getting Started
on the Numbers"
(13)
provides a methodology for managers not necessarily deeply
knowledgeable of the mathematics or economics of option pricing theory with a way to
do easy real option value estimates. Like Leslie and Michael's paper it relies on the
foundations laid out by the Black-Scholes equation to provide the intuition and
methodology. Nevertheless Luehrman develops a transformed version of NPV (called
NPVq) that together with a measure of "cumulative volatility" -which incorporates
volatility and time- provides all the information available in the five basic Black-Scholes
parameters. These two parameters in turn are used to look up in a table the value of the
option as a percent of the "stock" (present value of underlying assets).
Kulatilaka and Perotti develop a mathematical model for real options in markets
with imperfect competition in their (1998) paper "Strategic Growth Options" (").In it the
authors prove that acquiring strategic growth options can serve as a powerful deterrent
for competitors to invest in capacity or even enter the market and therefore results in the
option holding company having a greater market share and a lower cost structure, as is
seen in many technology markets. This result is dependent however on the level of
"strategic advantage" intrinsic to the product or service market.
2-11
Laura Quigg's (1993) "Empirical Testing of Real Options Models" (1)
is the
second empirical work to prove that investors do value real options and act in a rational
economic fashion as the theory would suggest. Her work is based on the study of
Seattle's land market.
The only preceding empirical work was Paddock, Siegel and
Smith's (1988) "Option valuation of claims on real assets: The case of offshore
petroleum leases"
(16)
which concentrates in offshore oil production licenses.
Two Harvard Business Review papers on new economy uses of real options
theory are N. Nichols "Scientific management at Merck: An interview with CFO Judy
Lewent"
(17)
and W. Sahlman's "How to write a great business plan" (18). These two
papers give practical examples of the uses of real options within the contexts of R&D
projects in a biopharmaceutical company, and the valuation of startup ventures from the
point of view of the venture capital community. They are among the more recent
examples of practitioners pushing for the dissemination of real options theory among
their colleagues.
For complete treatment of real options theory Amram and Kulatilaka's Real
Options (19) is an excellent text. They condense many of the ideas developed by others
and themselves over the past decade and a half and published in research papers into a
single readable volume. It also includes an excellent list of references to the papers and
texts they used. Older works that concentrate on real options are Flexibility, Natural
Resources and Strategic Options (20) by Brennan and Trigeorgis, Real OptionsManagerial Flexibility and Strategy in Resource Allocation (21 ) and Real Options in
CapitalInvestments: Models, Strategies and Applications (22) both by Trigeorgis, as well
as Investment Under Uncertainty
(23)
by Dixit and Pindyck. Two treatments of real
options in valuation and corporate finance texts are "Using Options Pricing Methods to
Value Flexibility" in Valuation, Measuring and Managing the Value of Companies by
Copeland, Koller and Murrin
(24)
and "Applications of Options Pricing Theory" in
Principles of Corporate Finance ( ) by Brealey and Myers. For more basic readers a
good introductory book to valuation that does not go as far as including real options is
Business Analysis and Valuation Using FinancialStatements (26) by Palepu, Bernard and
Healy.
2-12
3 Real Options Review
3.1 Uncertainty, Flexibility and the Law of One Price
Net present value (NPV) is the most commonly used technique for valuing
investment projects today. It states that the value of investment projects must equal the
sum of all expected cash inflows and outflows the project will generate properly
discounted at the project's cost of capital:
NPV = MAX[r E(CashFlow)
t=O _CostofCapital
]
Equation 3-1: The meaning of net present value.
The cash inflows include all cash revenues and the outflows include all cash
expenses and capital expenditures necessary to earn the revenues. The net present value
technique works best when these inflows and outflows projections are as accurate in time
and magnitude as they can be to the future outcome of their values. The cost of capital in
turn includes the weighted expected returns of investors of all debt and equity that the
firm has issued for the project. This risk-dependent weighted cost of capital should be set
as close to possible to the real return that investors expect. Estimation of both cash flows
and cost of capital is often fraught with problems due to the use of most likely -i.e.
median, not expected- cash flow scenarios, worst-case cost of capital requirements, and
other common biases. Properly addressed they can be avoided, but biases and interests
often work together to ensure that in some applications NPV estimates are often far from
the future outcomes or objective expectations. In addition, due to neglect, NPV is often
misused in another way. Rarely is account taken of the cash flow impact that the project
under study will have in other current company projects and vice versa. Like with the
cash flow and cost of capital issues however there is no fundamental reason why the
technique itself is at fault here. In principle all three problems can be avoided with proper
care.
There is however a fourth complication that NPV applications encounter and it is
how to include the project's impact on future company business. NPV assumes that there
is no uncertainty, and therefore that either we can reasonably predict any impact that the
project will have in future operations or that there will be no impact to worry about.
3-13
Because of this -NPV says- we can take final investment decisions today with total
confidence in the most profitable outcome and no possible impact -positive or negativein any future operation outside of the project. All NPV based investment decisions can
thus in principle be, and are assumed to be, final since they do not accrue any possible
unknown benefit or cost to the company. The problem is that in practice the certainty
assumption breaks down since valuators do not know what the future could bring in terms
of markets, opportunities, competition, prices and other variables of interest. Therefore
how can they build an omniscient NPV model when they may not know what the future
may bring to the cash flow of the project itself? Recognition of uncertainty in the real
world is one of the reasons for the use of real options theory.
Once we have recognized uncertainty, another reason why NPV is at fault is that
management should be able to act flexibly to the now uncertain outcome of future events.
As we noted NPV also assumes finality of investment decisions, even of those to be
expended in the future, once we have committed to a project. To tackle both these issues,
an alternative approach to NPV called decision tree analysis (DTA) allows for both
uncertainty and managerial flexibility. It is based on a tree like structure of the future,
where each branch of the tree represents one possible future outcome and the
corresponding managerial decision that maximizes firm value. Each branch is assigned an
outcome probability and value is computed by probabilistic expectations. So if DTA
deals with future uncertainty and managerial flexibility why is it not yet enough?
DecisionTreeValue = E[MAX( CashFlow ,0
t=t CostofCapital
Equation 3-2: The meaning of decision tree analysis.
The answer is that DTA does not take into account the third and final reason why
NPV fails to match the accuracy of real options. Neither accounts for investors'
opportunity to trade and borrow in the financial markets. The basic premise behind this
opportunity is that there exists a portfolio that an investor is able to construct through
financial and investment operations that should give rise to exactly the same payoff as the
project itself. Because this portfolio and the project are economically indistinguishable
they should be worth the same, or else arbitrageurs will bid up one and down the other
until there are no more risk-less profits to be made from the operation. Therefore after no
3-14
more than a finite amount of time the law of one price must hold. DTA -although it
recognizes uncertainty and flexibility- does not enforce the law of one price.
We conclude that NPV fails to describe the time series relations between projects
on three counts -uncertainty, flexibility, and the law of one price- and that DTA, an ad
hoc correction to NPV, still fails at properly describing the time series relations through
the failure to adopt the law of one price. Real options theory properly addresses all of
these issues. This does not mean that NPV and DTA are useless theories that should be
discarded altogether. As we will see later derivatives of NPV are still needed as a
valuation tool for safe cash flows that have little impact on other company operations.
NPV and real options merely describe different aspect of the company. Similarly DTA
may serve as a useful shortcut to approximate real options values when necessary
information is lacking, or the precision of the project value figure may be less important
than arriving at a quick and easy estimate. As for real options it should be noted that
although it is a great valuation tool its worth extends beyond it to include its implications
for corporate strategy.
3.2 Option Fundamentals
Above we have showed why the NPV rule is not appropriate to value many
company projects and why a real option model is needed to correct for its deficiencies.
Now we need to review some of the basic properties of options, so as to understand how
their value arises.
An option is a contract that gives its holder the right, but not the obligation, to
execute a transaction at or before a certain date. Common types of options are the options
to buy or sell financial assets publicly traded in the financial markets, the options to
purchase common stock often awarded as part of compensation packages, and contractual
options to purchase durable goods and real estate. Of these the later are in fact real
options, in that they represent the right to purchase a real asset. Other real options are the
right a company has to develop a new product, based on research that has been done in its
labs, or the right to distribute an existing product in a new market. The ability of
companies to adjust production levels can also be modeled as a portfolio of options, and
many other examples abound.
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3.2.1 European versus American Options
There are two main types of options as classified by when can they be exercised.
If the option holder has the right to execute the transaction at any date before expiration,
the option is called an "American" option. On the other hand, if the option holder only
has the right to exercise the option at the expiration date, the option is called a
"European" option. American options are commonly seen traded in financial markets,
though both types of options are common imbedded in contractual clauses. Real options
also come in both flavors, but just like financial options it is common to assume all
options are European for simplicity of computation. This is motivated by the fact that
only the payoff at maturity needs to be known for European options, since the European
option holder can not realize any other payoff before that date.
3.2.2 Call and Put Options
An even more important taxonomy of options is whether they give their holders
the right to buy or to sell an underlying asset or cash flow. A "call" option gives its
holder the right to buy the underlying asset at a specified price -the strike price- in the
future at or before a certain date -the expiration date. Because of this a call option has
nonzero value at the expiration date if the underlying asset is worth more than the strike
by the exact difference of these two values. The possibility of the payoff from the call
having a positive value in the future gives the instrument a positive value today even if its
current payoff would be zero. Similarly the possibility that the payoff from the call will
be even greater in the future gives the instrument a value greater than its value if
exercised profitably today. Thus calls are always worth at least as much as their current
payoff but greater than this payoff before the expiration date. Most types of practical real
options are modeled by call options. These include options for growth, deferred
investments, expansions, extensions, etc.
The other type of option, called a "put" option, gives its holder the right to sell an
underlying asset at a specified price -the strike price- in the future at or before a certain
date- the expiration date. Thus a put option has a nonzero value at the exercise date if the
underlying asset is worth less than the strike price by the difference between the two. And
just like call options put options are always worth as much as their payoff but more so if
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there is still time remaining till the expiration date. Common types of put real options are
exit options, options to contract, and options to shorten the life of assets.
3.2.3 Long and Short Option Positions
One key characteristic of options, like any financial asset, is that they can be
bought -also called to long an option-, and that they can be sold even if we currently do
not own the option as long as we make a promise to deliver it upon request, or
alternatively deliver immediately a borrowed option that we must replace -this is called to
short an option. Thus we can create not only a net positive -or long- exposure to options
but also a net negative -or short- exposure. Holders of short positions are bound
according to the rights and wishes of the long position and therefore they must receive a
payoff for their trouble. The payoff they receive is the value of the option, which they
receive from the long position in order to create the contractual obligation. In the case of
"synthetic" real options -or options that are not part of a contractual agreement between
two parties- there often is no clearly defined short position. This short position really is a
portfolio that is distributed among various holders in the markets. Nevertheless short real
option positions do exist in contractual agreements and it is a known fact to us that the
value of the option must be the same to the short and long position.
3.2.4 Option Payoff Diagrams
The payoff of options can be visualized using diagrams. These diagrams represent
the potential cash value of exercising the option at the expiration date as a function of the
value of the underlying asset "S". Their main characteristic is the presence of the strike
price "K" at which there is a kink, or change in slope, of the payoff function. For a long
put there is a 45 degree line prior to the strike price commencing from a value equal to
the strike price itself -the value that the option would have if the price of the underlying
asset at the expiration date where zero- to a value equal to zero at the exercise price and
after. For a long call the forty-five degree line begins at the strike price, since a call is
worthless at the exercise date if the price of the underlying asset is less than the strike
price and after the underlying asset surpasses the strike its value grows linearly with the
asset.
It is also possible to visualize the payoff to holders of short positions. Given that
payoffs are symmetrical to longs and shorts, that is that the earnings of a long are the
3-17
losses of a short and vice versa, the payoffs of shorts are the S axis reflection of the
payoffs to longs. Thus short calls have constant positive payoffs until the value of the
underlying asset reaches the strike price at which point the payoff starts decreasing dollar
for dollar with the rise of the underlying asset value. Similarly the short puts will have a
positive payoff above the strike price but their payoff will decrease dollar for dollar with
each dollar decrease in the price of an underlying asset.
Profit
Profit
K
0
)
*K
*
*
0
P
C
Loss
Loss
Long Call
Long Put
Profit
Profit
>
C
0~
K
S*
0)
Loss
Loss
S*
K
Short Put
Short Call
Figure 3-1: Payoff diagrams of long and short call and put positions. C and P are the prices paid for
the options, K is the strike price, and S* is the value of the underlying asset at the expiration date.
Note that short positions are mirror images of long positions over the S* axis.
3.2.5 Option Portfolios and Fractional Options
Options may in fact be grouped together into portfolios. In financial markets this
is often done in order to construct specific payoff scenarios that would not possible by
simply taking long or short positions in single calls or puts. Thus for example a short put
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and a long call with the same strike may be used to construct a long forward position. A
long call and a short call with different strikes may be used to construct vertical spreads.
Also a long call and long put with the same strike price may be used to construct a
bottom straddle. All of these are examples of synthetic derivatives: an instrument that can
be composed of elementary long and short put and call positions.
In the real options world put and call positions can also be combined together
with positions in their underlying cash flow to create desired payoffs. Thus a company
may hedge its risk exposure to changes in the price of a required input by using a
combination of puts, calls and the productive asset that resembles the payoff of a vertical
spread. This is the case of switching and scalability options in which the company that
holds them can use long calls to initiate the use of productive assets, and short puts to
terminate their use. As we will see later when studying scalability options, Dell
Computer's just in time manufacturing process is a real time use of the scalability option
it holds on its productive assets.
A portfolio of options may in fact contain just fractional options. In financial
options such a portfolio may be composed by buying a certain number of options, say
ten, and then selling interests in such portfolio piecewise, say to twenty interest holders.
In real options they arise naturally due to fact that some of the benefits of the changes in
the price of the underlying asset accrue to other parties other than the option holder. The
main property of fractional option holdings is that changes in the payoffs are no longer
dollar-to-dollar with respect to changes in the underlying asset, but rather some-numberof-cents to the dollar. Thus for example the holder of half a call on the revenues of a
certain microprocessor will only receive half a dollar for each extra dollar that the
revenues exceed the strike price. Therefore it serves to model the effect of costs of goods
sold and other associated project variable expenses on the increased revenues of
companies. Thus in the case where the underlying cash flow or stock is used to model the
revenues of a project, the strike price is used to model the fixed costs, the the ownership
of just a fraction of an option is used to model the variable costs.
In terms of their value half an option is only worth half a full option, and each
fraction is only worth whatever fraction of an option it is. The valuation significance of
this realization is that Software and internet media firms, or any firm that sells pure
3-19
information, that generally own full options since their variable costs are practically zero,
should sell at higher multiples than Hardware or internet retail firms, who incur
substantial variable costs for each extra unit sold and thus own only fractional options.
Interesting cases in point are Intel and Microsoft each of which has comparable revenues
and similar R&D expenditures -a proxy for fixed product costs. Of the two Microsoft has
traditionally commanded a higher multiple in order to take into account its lower fixed
costs (lower strike) and higher gross margins (larger fraction of an option).
The issue of fractional options has only left us with one question to answer. Like
in financial options, can anybody own more than one (identically equal) real option on
the same cash flow? The answer is no because in our model where S represents the
potential revenues of a project it is impossible to construct a cost structure for the project
that will leave the company a profit greater than its revenues. Financial leverage might
increase return on equity investment, but that figure is not to be confused with gross
margin or net income for the project.
3.2.6 Put-Call Parity
The relationship of put-call parity allows us to value the right to sell a cash flow if
the value the right to buy it is known. Conversely it allows us to value the right to buy a
cash flow, if the value of the right to sell it is known. In financial options its significance
is that if the price of either a call or a put and its associated stock and debt securities are
known the value of the other option can be deduced without resorting to first principles. It
also has the value that in the case where there is mispricing by the financial markets it is
possible to clearly see the arbitrage opportunity to be taken advantage of.
C
=
P+ S
-
D - K * r-
Equation 3-3: Put-call parity relation. Allows us to value the call of an asset with a strike price equal
to that of its corresponding put if we know the value of this put, plus the present value of the asset
and the price of a risk less bond of the same maturity as the options.
The potential significance in real options of the put call parity is analogous.
Should we know the price of either the put or a call on a project we should be able to
price the other, and if we have the price of both we should be able to check for arbitrage
opportunities.
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3.3 Option Pricing Theory
We have reviewed many of the fundamental properties of options. What are there
basic types, what we can do with them (long or short), what kind of payoffs they have,
etc. Now we proceed to review pricing methods. Though what we studied in the previous
sections is of invaluable help in understanding options and setting up option valuation
problems we also need to have the computational tools necessary to price option projects.
This we will achieve mostly through the use of the binomial method. We will also
provide the Black-Scholes formula and its strategic meaning as part of this subchapter.
3.3.1 The Binomial and other Decision Tree Option Pricing Methods
The binomial method is based on three main premises that also serve to inspire
the method of solution. Our options are written on an underlying asset or cash flow "S",
often call the "stock" or "commodity", that changes value at discrete units of time in a
discrete fashion and that such price changes are out of the control of the firm. In other
words this asset or cash flow operates in a perfectly competitive commodity like market.
The second premise is that management reacts to these changes in price in an
economically rational manner. Thus they choose to exercise their options only when and
always when it is optimal. The third is that investors have the ability to construct a
market portfolio that exactly replicates the payoff of the option and that therefore they
will only be indifferent to buying the portfolio or the option when they are priced the
same. Recalling subchapter 3.1 we see these three premises in fact correspond to the three
reasons why real option valuations can be more accurate than NPV methods. But
moreover these three methods correspond to the three main elements and steps in the
binomial method solution process that we will describe below.
3.3.1.1 The Event Tree
The binomial option pricing method is based on the simplest possible
representation of the change in price of the underlying asset. Two of its main assumptions
are that the underlying asset can only change price in discrete units of time of equal
interval and that in such price changes it can only take two new possible prices: hence the
name binomial. In its simplest possible case there is only one time period and the stock
price change can be represented by a starting price and two ending prices: like the root, or
3-21
node, and the two branches, or leafs, of a very simple tree. We'll call this a unit tree.
However when there is more than one time period the price change process charts out a
tree where the leafs of the preceding unit tree are the node of a succeeding one. As the
number of time periods increases to infinity the underlying asset can experience any price
change within a broad range of numbers with the most likely final figure along the
middle values. The visual diagram that represents this behavior is called a binomial event
tree.
SUU121
25%
100
50%
Sdd 83
25%
SU 110
S $100
d91Sud
Figure 3-2: Binomial event tree describing the price change over two time periods of a 10 Gigabyte
hard drive. At time zero the price of S -the hard drive- is $100. It can rise 10% or fall 9% (d=l/u) in
each time period. It is twice as likely -50% - to finish the cycle unchanged, as it is to experience a rise
or fall in price -25% each.
More generally any diagram that describes discrete possible changes of market
variables in discrete units of time is called an event tree and is the first step in solving an
options pricing problem by the binomial method. Event trees generally describe the
market behavior that is not under the control of the firm. It need not necessarily be
binomial, and all branches need not all terminate at the same time period.
Its main
characteristic should be however that it includes all relevant information pertaining to the
underlying asset or cash flow that we wish to study. Thus any structure that has a single
starting stock price and that has a finite number of branches that it can reach over a finite
number of possible steps is an event tree. In the example figure above we see the price
change of a 10 Gigabyte hard drive over a two-month period. The example is modeled as
a simple two period binomial tree in which the price of the drive can rise or fall
approximately 10% at the end of each of the two periods, resulting in three possible end
3-22
prices out of which the middle end price -which corresponds to the beginning price- is
twice as likely as either of the other.
One caveat of event trees is the assumption that the progression of the asset
market is out of the control of the firm. This is certainly the case for commodity markets,
but may not always be the case in subtle ways for technology products. Even so in the
technology arena there are many commodity like goods. The dynamic random access
memory (or DRAM) and the hard disk drive market used in the example are two of those.
Moreover even in the case of more value added products like cutting edge Internet routers
consumer demand is largely out the control of the manufacturer and thus assuming that it
behaves in a commodity like fashion can only serve as a conservative approximation.
3.3.1.2 The Decision Tree
The next element of the binomial solution process -the decision tree- serves to
describe how does management react to the resolution of the uncertainty described in the
even tree. Generally decisions are taken only at the resolution of uncertainty points, but
often are not taken at all of these points. This is the case because often the end events are
the one interest, the time by which the option or options are assumed to expire. Even if it
is not the case, by whenever the option has expired, it has achieved a value equal to the
difference between the value of the underlying asset and the strike price of the option, or
zero which ever is greater.
C* = MAX (S * -K,O)
Equation 3-4: Value of a call at expiry.
"C*" is the numerical value that call options achieve at expiry on the price of the
underlying assets "S*". For each terminal leaf of an option C* will usually be different but may not be- and each of these C*s will be needed to compute the value of the call
today "C". With respect to the event tree the only new information we have gained are
the C* values, but these are of crucial significance since they embody the decision that
management has taken in order to maximize firm value. Thus when this information is
added to the event tree previously described we arrive at a new tree we call the decision
tree.
3-23
SS,C
SS C
Sd'
d
Figure 3-3: Elementary decision tree. The values of "S" and both "S*" are known from the event
tree. "C*"s are known from having taken the most profitable decision at the end of the relevant
period. Another variable "r"the risk less rate is generally always known, thus the only unknown is
"C", which is the value of interest.
With a decision tree completed we have all the relevant underlying asset prices,
and terminal leaves option prices, so that with knowledge of the only one more piece -the
riskless rate- we have all the information we need to compute the option value C.
3.3.1.3 Portfolio Replication
The portfolio replication principle is the third and final piece necessary to
compute real options by the binomial method. It states that to find the value of the option
we can create a portfolio that produces the exact same payoff at the end of the relevant
period as the option itself and compute the value of this portfolio instead. To do this we
are allowed to lend and borrow in bonds "B" at the risk less rate "r" and we are allowed
to invest in a twin security or stock "S" that has perfect correlation with our option. Thus
the one period binomial option pricing method can be stated mathematically in the
following formulas:
C* =f(S*)
N * SU + (1+ r)* B = Cu
N * Sd (1+ r)* B = Cd
C=N*S +B
Equations 3-5: The binomial equations that relate the values of a single period call, stock and bond
through the law of one price. The first equation indicates that the future value of the call is a
function of the future value of the stock, the second and third that the value of the call and the
replicating portfolio must be equal on each state of the world, and the fourth gives the value of the
call today as a function of the value of the stock and bond today.
The first equation above states that the payoff of the call is a function of the value
of the underlying asset at the date of maturity of the option. The second and third enforce
the zero arbitrage condition which merely mean that a certain number of stocks "N" and
certain number of bonds must equal the payoff of the call at the maturity date in each
3-24
possible state of the world. Finally the last equation gives the value of the call today on
the basis of the value of the stock and the number of stock and bonds today. The two
middle equations can be solved for the variables in the formula for computing the option
value of interest into the following two middle equations:
C*=f(S*)
N= CU -Cd
SU
-Sd
B = CU - N *S
1+r
C=N*S + B
Equations 3-6: The binomial formulas to compute the value of a one period call using a replicating
portfolio. These equations have been solved for the number of stocks in the replicating portfolio and
the value of the bonds in the portfolio today.
These equations now state the number of stocks as a function of the value of the
stock and the payoff at maturity, and the number of bonds as a function of the stock up
and call up values, the number of stocks and the risk free rate. One key insight from using
these intermediates is that we notice that often our net bond position is negative. That is,
we are short on bonds. This is the case because to replicate the greater returns of options
over stocks we need to borrow money to finance the stock we purchase, thus leveraging
our position.
Armed with portfolio replication, we can now use all the pieces we found in the
event and decision tree parts of the solution process and compute the value of the option
by means of the binomial method.
3.3.1.4 The Binomial Probability Formulas
In essence what portfolio replication states is that all investors act indifferently to
risk and will therefore assign a unique value to the same option given fair market prices.
Since another way of seeing binomial options is that they are a security whose value is
the expected payoff given that there exists two distinct states of the world, the implication
is that there exists a precise risk neutral probability "p" and exclusive probability (1-p)
that each of this states of the world will occur. And given that both the option payoff and
the underlying asset obtain well defined values in exactly these two states it is possible to
derive the probabilities from knowledge of current fair price of one or the other. The two
equations below describe this relationship.
3-25
" *CU +(1-p )*Cd
1+r
C=
(1+r)*C-Cd
Pu =
"
C -Cd
Equation 3-7: The binomial probability formulas. The first equation states the value of a call as a
function of its risk neutral probabilities. The second solves the first for the probability of an upward
movement
There is one particular version of the binomial price movement that is very widely
used. In it we strengthen the assumptions that the asset can only make two changes in
equal discrete units of time by forcing these changes to be one up and one down and
having them be inversely related to each other. In other words that the multiplicative
factor of the up movement (u) inverted gives rise to that of the down movement (d=1/u).
In this case we have more stringently defined binomial probability formulas which are
related through these up and down parameters, or a derivative of them that uses a variable
we'll call the volatility "cr". These formulas are often used to model stock and
commodity price movements in the financial markets.
u = ea;d = e-C
era -d
Pu =
u-d
ewAcc-a
q,=
-d
u-d
Equation 3-8: More binomial probability formulas.
It should also be noted that the computed risk neutral probabilities are not the
same as the actual observed probabilities. Nevertheless we can arrive at the observed
probabilities by inserting the project's cost of capital in place of the risk free rate while
using the same parameters in the rest of the formula.
3.3.2 The Black-Scholes Method
The Black Scholes formula is the preferred method of computing the value of
traditional European and American financial options of a single contingent variable since
it describes in closed form the price of an option from six fundamental determinants. The
formula is nothing other than the result of solving the option partial differential equation
subject to the boundary constraint that at the exercise date the price of the option should
3-26
be equal to its payoff. The formula is also subject to the law of one price, which says that
no investor will pay different amounts of money for two investment opportunities that
give right to the same payoffs in the same states of the world.
C = Se-" *{N(d1)}- Ke" *{N(d2)}
In S+
(r -8 +0.5
*
.2)
d=
d-*t
d 2 =d -T* '
Equation 3-9: The Black Scholes formula for an American call of one contingent variable and with
dividends.
Above we have the Black-Scholes price equation for an American call taking into
account the value of the option lost to dividends. Some of the parameters are the same as
in the binomial model. "C" is the current price of the call, "S" is the current stock -or
underlying asset- price, "r" is the risk free rate, "K" is the strike price, "t" is the time to
expiry, "(-" is the stock volatility, and "S" are the dividends payed. "d1" and "d2" are
intermediate values that are used to compute the cumulative probability distribution
functions N(di) and N(d 2 ).
In order to compute a real option value using the Black-Scholes formula we
would need to find or estimate all of the six inputs parameters. These parameters are
unfamiliar and are quite unlike the sort of numbers we are used to estimating in NPVs or
binomial calculations. In some cases, such as the stock/cash-flow volatility it may be
impossible to have a good estimate altogether. While it is not the case with options on
continuously exchange-traded equity, it certainly is with options on cash flows that may
not exist yet or that if they do exist are at best reported every three months. Thus unlike
the binomial method the Black-Scholes one may not have much application in most
practical valuation situations.
Nevertheless it does have strategic value, precisely because it focuses on the six
factors through which managers can influence option value in their companies. With an
understanding of the mechanisms by which managers can influence the parameters in the
real world, they can enhance the value of the options their firm is holding. We thus
proceed to explain the significance and influence of each parameter on option value from
a strategic perspective.
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3.3.2.1 Risk free interest rate "r"
The risk free interest rate is of special interest from real options point of view
because contrary to its impact in NPV calculations -where it enters as an input to cost of
capital via the capital asset pricing model or its alternatives- a rise in interests results in a
rise in the value of the option.
The logic behind is that a rise in the interest rate deceases the present value of the
exercise price of our option. To see how this is the case recall equations 3.6. The middle
equation, which is used to compute the magnitude of the number of bonds we need to
replicate the option, indicates that the greater the interest rates the lesser the number of
bonds. But now recall the bonds are usually part of the replicating portfolio as shorts.
Thus the fewer short bonds the lesser will be our debt and the greater will be the value of
our call.
The primary lesson is that it may counter to real options logic that prices of
uncertain projects or companies should fall when interest rates rise -if everything else is
held equal. For managers and investors this may be of significance to their activities in
situations where the central bank is aggressively rising interest rates to stave off inflation
and seemingly bringing down with its actions the equity prices of growth companies.
This is what has happened in the Nasdaq stock market, whose composite index fell from
over 5,000 in March 2000 to below 2,300 in January 2001 as the US Federal Reserve
raised interest rates from 5.5% to over 6.5%.
Nevertheless it also important to note that options' value sensitivity to interest
rates is among the smallest of all parameters. Thus when such a phenomena as we
experienced over the course of the last nine months occurs it may be more appropriate to
justify it through other parameters, as we will see below. Moreover the risk free interest
rate, although under the control of national central banks, is completely out of the
influence of private companies and investors unless they can lobby to influence monetary
policy.
3.3.2.2 Value lost over duration of option "8"
The value lost over the duration of an option is the equivalent to the dividend paid
by stock in the case of financial options. It is the value investors loose as claimants of
underlying the cash flow due to its distribution to other claimants. In the case of real
3-28
options it could be the customers or market share or positioning companies loose to
competitors for failing to preempt their entrance, or it could be the maintenance cost
needed to incur in order to keep company options open.
The value lost over the duration of an option is a parameter that is not present in
any form in NPV models. In binomial models it is present through an adjustment that
decreases the price of the stock or cash flow and the call payoff by the amount of the
dividend at the payment date. Like the risk free rate of interest its impact on option value
is generally small, but unlike it, since dividends represent loses to option holders, a rise in
dividends results in a fall in option value.
The presence of dividends losses is one of the reason competing firms often rush
to enter new markets rather than wait for the outcome of the contingent event. It may be
possible to influence this parameter of real option value by eliminating the dividends
losses directly. If a firm manages to contractually lock in key customers, or to impose
regulatory constraints on competitors, it may in effect manage the reduction or
elimination of its dividend losses.
3.3.2.3 Time to expiry "t"
The time to expiry of a real option corresponds to the exact same parameter in a
financial option. It is the amount of time during which the option can be exercised. Like
in financial options an increase in the time to expiry will increase the value of the option
since it increase flexibility. In fact an option has positive opportunity value because its
time to expiry is greater than zero: An option with zero time to expiry has a value equal
only to the stock price minus the strike price or zero, which ever is greater.
However unlike in a financial option the time to expiry of a real option is
sometimes a fussy concept. It is not so when it is based on some contractual right that a
company has acquired from a government, another company or elsewhere. For example
company A may grant company B the option to use part of A's manufacturing capacity
between a certain (usually close to present) date and another certain date in the future (of
for example five years). In this case the two companies can value the given option as an
American call (because it can be exercised at any date before expiry) with a known
expiry date. But what would happen if the option in question a company owns is not
contractual, but on the other hand is a market option? For example,
3-29
if a
biopharmaceutical company has an ongoing R&D project that may have useful
commercial value until the product becomes obsolete how does the company known
when does this obsolescence date occur? The answer is that the project valuators must
make an estimate of useful life of the option on a case-by-case and understand that such
number is nothing more than a presumably educated estimate.
Of more significance is the fundamental fact that options are contracts that expire.
A company that currently enjoys the benefits of owning a growth option can not expect to
own it at perpetuity, though in some circumstances it may be the case. For example a
company that owns the exclusive rights to some proprietary technology can expect to
have the monopolistic right to use this technology to generate revenues only as long as a
competitor does not develop a functionally equivalent alternative. If a competitor does
develop and alternative, then the option to profit from it may be greatly reduced or even
destroyed. Thus companies can increase their value by extending the time to expiry of the
options they hold.
Another key fact about time to expiry is that though it has a greater impact on
option value than both the interest rate and dividends, it nevertheless is another parameter
with relatively little effect on option price.
3.3.2.4 Volatility of expected cash flows "oy"
The volatility of expected cash flows corresponds with the volatility of the stock
or commodity price in financial options. Like the time to expiry it is also of fundamental
value to the existence of the option. If there were not volatility -the quantification of
uncertainty- there would be no value to having the right but not obligation to perform a
certain transaction. We would already know how much would the underlying asset be
worth by the time to expiry and thus we would know with certitude how much we would
need to pay today for the certitude by discounting at the risk less rate. Also like the time
to expiry an increase in volatility translates to an increase in option value, but volatility
has a bigger impact than "t".
Nevertheless, even more so that "t", volatility is perhaps the hardest to estimate of
the parameters in a Black-Scholes real options formulation. In the case of financial
options volatility is generally computed as a moving average of underlying asset
variances or standard deviations from a certain number of most recent periods. Thus for
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example the daily price changes of a stock for the past year may be used to estimate its
daily volatility as of today. But in the real options world we are generally dealing with a
cash flow that is unique, relatively unknown -perhaps without history- and does not trade
continuously on any financial market. Thus how to compute its volatility? Just like with
time to expiry reasonable estimates can be made by using quarterly cash flow information
-or that of shorter times periods if available, using the stock price volatility of single
project competitor firms, or using other proxies. Thus for example we may decide that if
we are trying to compute the volatility of the free cash flow for a toy internet retailer and
we have the volatility for the free cash flow of a book internet retailer then we may use
the value of this second as a proxy of the first, perhaps after some adjustment. This
adjustment in turn may be estimated by seeing the relative volatilities of the free cash
flow for brick and mortar toy retailers versus bookstores.
But we should not forget that it is the strategic understanding what we care about
the most. Thus a company that holds real options can enhance their value by increasing
the volatility of their expected cash flows. This conclusion, like others before in the real
options framework, is at odds with NPV thinking. But we can see how this is clearly the
case by going back to Equations 3.6. We note that the number of stocks "N" we need in
the replicating portfolio is directly proportional to the difference of the payoff in the case
where the stock goes up and the case where it goes down (Cu-Cd).
3.3.2.5 Present value of fixed costs "K"
The present value of the fixed costs of the project is the counter party to the strike
price in a financial option. In real terms it represents the incremental capital expenditure
that must be incurred in order to gain access to the underlying free cash flow. Thus for
example if we have a project where some capital expenditure has already been incurred to
purchase the option to further the project, then the second round of capital expenditure
that would be required to finalize the project is represented by the present value of the
fixed costs. An increase in this parameter decreases the price of the option since more
money has to be paid. It tends to have the second largest effect on the price of an option
for any given magnitude change of itself.
To compute these costs an estimate must be made at the date of the expenditure
and then that value must be discounted back. It is important to note that these fixed costs
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are estimates but it is even more important to note that they are expected values that
change over time. Even more so, they change not only by the passage of time but by the
changing of technology, markets, and even by actions the management of the company
can take. It may be the case that the development of a new manufacturing process, or the
change in prices of certain raw materials, or other market actions may lower or raise these
fixed costs. Thus the primary way of managing the value of company options through
managing their strike is to lower the strike price through research and development,
developing efficient manufacturing processes, or setting up good distribution networks.
3.3.2.6 Present value of expected cash flows "S"
This component of a real option is the most like its equivalent in a traditional
discounted cash flow valuation. It represents an estimate of the cash flow of a project
discounted back to the present. It also corresponds to today's stock or commodity price in
the case of financial options. An increase in the value of the expected cash flow results in
an increase in the value of a call option on it. Moreover, of all six parameters expected
cash flows is the one that has the greatest impact on option value.
From a managerial point of view increasing the expected inflows or decreasing
the expected outflows can serve to maximize option value. An important way of doing
this is by cascading the investment opportunities that the current option we hold
generates by including in its payoff another option. This in effect creates what is called a
compound option described below.
The ways a company seeks to maximize the cash flow resulting from its
investments includes marketing the product to a larger audience -for example expanding
from the home PC business to the corporate sector, or going international. It also includes
finding new applications for products the company currently has such as Microsoft's
efforts to universalize windows as an operating system to include servers, palmtops and
other types of devices.
3.4 Types of Options by Structure and Application
One of the most important pieces of knowledge we can have for the use of real
options is a basic standard set of project options and their combinations that we can
identify and match with commonly occurring examples. This can be done since as we
have seen earlier from a properties point of view there are only two types of options, calls
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of puts, and that each can only be either bought or sold, resulting in only four basic
combinations. Nevertheless we rarely observe short real option positions, thus long call
and put positions give most of the examples of the use of real options. Moreover the
single most common of these combinations is simply going long with a call, which means
that once we know its most popular uses we have a very powerful tool. Nevertheless as
we will see portfolios of options are common, making this would-have-been simple
problem a little more elaborate.
3.4.1 Single Option
The simplest possible project or company to evaluate is that where there is a
single time period, a single contingent event, and a single binomial decision based on this
event. In this situation management has committed capital at the beginning of the period
in order to obtain the right to buy or sell a certain cash flow by committing more capital
at the end of the period.
Expected Cash
Flows Scenario I
Fixed Costs
Expected Cash
Flows Scenario II
Figure 3-4: The single real option. This option covers one time period and has only two possible
outcomes, thus following the pattern of a unit binomial option. It can be either of a call or a put and
it can be used for any of the possible applications described below.
3.4.1.1 Growth, Deferral Expansion, and Extension Options
There are four basic types of single options, as described above in option
fundamentals. Having a long call position is the most common of these in the case of
both financial and real options and accounts for a majority of the applications in new
economy companies. It gives the company the right to acquire a certain cash flow by
paying an exercise price at or before the expiry date.
One of the reasons a company may hold call options is that it can give the
company the right to pursue a path to growth in the future. Usually these paths to growth
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are made possible by technological or marketing investments that result in capital
knowledge, positions or networks that only require an incremental investment to give rise
to substantial payoffs, thought these payoffs may be highly uncertain. Examples include
R&D investments, corporate image marketing campaigns, and even entire technology
based startup companies. When the founders of Akamai Technologies chose to invest
venture capital in further developing the routing algorithms that are at the center of its
services they were investing in the growth option to later capitalize on the gained
knowledge to create a useful service that can be sold at a profit.
Growth options need not be internal or supply driven investments. Often
companies invest in their customers or suppliers, partners or even competitors in order to
acquire an option for growth. Sun Microsystems recently made an investment in Storage
Networks in order to capitalize the provider of data storage services so that it could grow
and proceed to purchase Sun's storage systems required for this growth. In doing so Sun
was investing in a customer that would grow its revenues potentially much more than its
investment had been. Gateway also has invested in its customers by given computer
illiterate individuals seminars held at the company's Country Stores in the use and
benefits of computers. Thought the company has branded the seminars as "community
service" it is clear they have the potential to increase demand of its products.
Acquisitions in fact can be thought of options for growth. Cisco Systems has put
in place one of the best acquisition and integration processes in the whole technology
industry. After developing the first Internet router the company has used the cash flow
generated by its success to fuel further expansion through acquisitions of new
technologies and products that could capitalize of Cisco's marketing and administrative
resources to achieve success. In effect Cisco has outsourced its R&D to the startup
market, and has acquired the most promising projects in order to maintain its own growth
and the high valuation that goes together with companies heavy in option phase projects.
Another of the uses of long call options positions for companies is in the ability
they give to defer further investments. This in a way can be seen as another interpretation
of the same growth strategy outlined above. Rather than commit all of the funds
necessary to grow today, a company may choose to only invest a part today, enough to
create the platform from which a final round of investment might serve to derive the cash
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flow. Venture capitalists use this type of option frequently when doing staged
investments in startups. By doing so, they irreversibly commit only a minimal part of
funds, while waiting for further technological and marketing information that will serve
to confirm the profitability of the second investment. The only catch is that VCs often do
their investing in more than two stages, resulting in the more complex case of
compound/learning options described below.
Expansion options give the holders the ability to increment already existing cash
flows by committing further funds to a project. This type of option is often used when a
small incremental expenditure serves to complete an extension to a manufacturing plant,
or to add a second distribution market to an existing product. An example is the case of
plant expansion at RF Micro Devices. The company recently completed a project to
create manufacturing capacity for its semiconductors for wireless applications with a
second stage project under way, after the revenues of the first part had proven that there
exists the necessary demand to justify the expansion.
Extension options are the fourth common use of long real call positions in
companies' portfolios. They give their holder the right to extend the use of assets by
paying an exercise price. Not so obviously in use by new economy companies, there are
often extension clauses in real estate lease contracts that have the economic properties of
real call extension options.
3.4.1.2 Exit -or Abandonment-, Contraction, and Shortening Options
Exit, contraction and shortening options are all examples of long put positions in
the real options world. An exit option gives its holder the ability to exit a project at or
before certain date in the future by paying an exercise price. It is the functional contrary
of the growth option and acts as an insurance against market or technological downturns.
Such an option can be of great value if a company has committed resources to a certain
product or technology that may become obsolete, displaced by a competing technological
standard, or pushed out of the market by a competitor's product.
Coming and Qualcomm are two companies that have exercised their exit options
in the recent past. The first used to be a diversified industrial manufacturer of glass
products, only one few of which were fiber optics and other high tech materials, that
divested through sales or closures all of its low growth business in order to concentrate
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on the more profitable lines. Qualcomm is a wireless communications company that first
exited the cellular handset business, and then the cellular networks infrastructure business
(through a sale to former competitor Ericsson) in order to concentrate on the more value
added technological standards business (the cellular standard CDMA being Qualcomm's
invention). Another company that has exercised an exit option recently was Lucent
Technologies, when it sold its power systems division to Tyco International. One thing
that is clear is that just as growth options can often be created by an acquisition, exit
options can often be exercised by a divesture. Thus there is a half symmetric situation
between the creation of calls and the exercise of puts in real options.
Contraction options are the functional contrary of expansion options. They give
the holder the right to diminish the scale of a cash flow in the case the economic
conditions should dictate that is the more profitable. Contraction options are common
within portfolios that contain expansion options. Dell Computer's just in time
manufacturing acts like a real time portfolio of expansion and contraction options,
constantly adjusting the rate of manufacturing to match the rate of present demand, thus
preventing the build up of any inventory and consequently saving company resources.
The final type of long put position, shortening options, are the functional contrary of
extension options. They give the holder the right to shorten the use of assets by paying an
exercise price.
Usually puts will be held in conjunction with the underlying cash flow. That is,
nobody will hold real puts "naked", or in other words, with the possibility of exercising
the option but not owning the underlying cash flow. Because of this the payoff of the
portfolio of interest, the put plus the cash-flow/stock, will be the sum of the payoff of its
two components. If we go back to what we learned in option fundamental's we'll
remember that this put plus stock combination has a payoff equal in shape to a long call.
3.4.2 Rainbow Options
Rainbow options are really just single options but are characterized by having
more than one contingent variable. For example a company may have the option to ramp
up manufacturing of a certain product if both the price and the quantity of the product
demanded exceed a certain threshold, thus in effect having a rainbow expansion option.
This type of options is seen often in commodity markets where the two variables of the
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example above -price and quantity- describe all that is to be known about the state of the
world.
In new economy companies rainbow options are in less obvious use since in
practice the summary variable of interest, total dollar demand, is the result of many input
variables besides price and quantity. This is the case because all products are not
identical, and competition though intense is not perfect. Moreover from a computational
point of view, it is very hard to obtain close form expressions for rainbow options of two
or more contingent variables. However computation by the binomial method sidesteps the
difficulty of finding closed form expressions for rainbow options, though now the
problem becomes constructing a replicating portfolio. Nevertheless rainbow options can
be useful in many situations when the company's options are indeed approximately
modeled by the resolution of more than one contingent variable. For example Quantum is
a storage devices manufacturer that operates in near commodity markets that must react
flexibly to adjust production to the two variables that summarize market conditions.
3.4.3 Compound Options/Learning Options
Compound options are options on options. These are perhaps the most important
classes of options because they give the right to further options at the exercise of the
current one. In other words the underlying asset of the current option is another option,
and may still also includes some cash flow, though not necessarily. Projects and
companies that typically can be described by compound options are staged investment
start-ups, and infotech and biotech research and development projects. In these the
investors choose to allocate a limited amount of funds at each stage and evaluate the
project advances at the end of a certain period or pending a certain market or
technological test, or clinical trial. The result of these evaluations is what determines if
the project or start up goes ahead with more funding or if the investment is terminated at
that stage. From an applications point of view these options are often known as learning
options. Learning options grant the option holder the right to test market conditions
before each successive stage of investment, therefore minimizing the chances of loss.
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First Round
Second Round
Investment
Financing
Financing
Payoff
Exit
\Exit
Figure 3-5: A staged learning option. This is an example of how a venture capital firm would fund a
two-staged company.
The compounds option approach is most clearly illustrated by the workings of the
venture capital industry. Venture capitalists most often do their investing in usually two
or three stages before an initial public offering (IPO). The advantage of this approach is
that the investments can proceed incrementally, only if the previous stages have proved
promising, therefore limiting the downside potential to investors. Thus a new startup may
first receive $1 million in venture funds for research, followed by $5 million to develop a
prototype if the research gives positive results, followed by a final $20 million to design
for manufacturing and set up an administrative, marketing and sales organization that can
distribute the product. In each stage there is the option but not the obligation to invest in
the next stage.
In fact the whole process by which many highly successful products in the
technological industries have been developed is inspired by compound/learning option
principles.
Microsoft's
Windows
operating
system
and
Intel's
x86/Pentium
microprocessor line have evolved through staged investments in each new version of the
product. This has forced the changes in design to be evolutionary rather than
revolutionary, ensuring backwards compatibility, building on the established platform of
applications, peripherals, networks and storage, and thus maximizing and fine tuning the
value for customers, the companies and the industry. These staged investments have been
in effect compounded call options. It is noteworthy that although Intel had success at
each stage of its strategy, Microsoft did not gain any significant market or profit from its
first two options -the first two versions of Windows- and nevertheless achieved great
profitability and almost total market share with versions 3.0 and later.
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3.4.4 Same-Project Option Portfolios
Flexibility -or Switching-, and Scalability Options
Option portfolios arise frequently in real options within certain contexts. For
example the single best financial description of many companies' R&D organizations is
that they consist of a portfolio of real options with each option representing a current
technology or process under development that may or may not be utilized in further cash
flow generating projects. These are an example of multi-project option portfolios, which
we'll study later. There are also portfolios of options on the same project, usually a
combination of puts and calls to ensure flexibility or scalability of operations.
The example we gave above of Dell's just in time manufacturing is a case of
scalability option, and in general any portfolio that guarantees the company that holds it
the ability to scale up or down in response to market conditions is another. Another
example of an option portfolio is an original equipment manufacturer (OEM), such as
Cisco, that subcontracts assembling to a electronic manufacturing services (EMS) firm,
such as Solectron. Should the OEM have the ability to move its manufacturing to another
EMS in case the original were to become uneconomical or face difficulties, the OEM
would in effect own flexibility options on its production. We thus see that much of real
options portfolios is about hedging.
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4 Valuing Projects and Companies using Real Options
In Chapter three we studied the principles of option pricing and real option theory
now we must develop and organized framework for valuing projects and companies using
real options. We will do this using the old problem solvers approach of divide and
conquer. We must divide the real options solution process into several parts, we must
divide our understanding of the industry and the company into several parts, we must
divide the company itself into several parts, we must compute the values of each part in
steps and finally we should bring it all together in the end to review the results by parts
and as whole.
C
D
ecom
om
p any
pose
C ash Flow Projec
C
om
p tio n P ro je c ts
w
p uteIII
kP rooje
ct
P roject Value
value
7
MTSU
otal
V alue
A naly se
Final Re sulit
Figure 4-1: The process of valuing new economy companies using real options and discounted cash
flow methods. The method is based on an analytical strategy where we concentrate in building
knowledge of the company by parts and then combining
redoing if necessary.
it all together, understanding the result and
What follows is a discussion of what we mean by new economy companies,
followed by a systematic approach to valuing said companies using a real options
framework. The approach contains cautions to avoid common pitfalls, suggestions for
visually understanding better the problem, and practical computational techniques to
arrive at actual prices. In the next chapter we'll demonstrate the principles valuing two
Internet infrastructure companies: Sycamore Networks and Check Point Software.
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4.1 Understanding New Economy Companies
The term "new economy" or its synonyms has been repeatedly used through the
history of economic progress. In general every time a technological revolution comes
along radically increasing workers productivity, improving the quality of life, and giving
birth to new industries dominated by newcomers that command substantial valuations in
the financial markets the term has been used. All of us are acquainted with its use in the
1990's particularly the second half of the decade during which pure play Internet
companies began to go public. The first of these was Netscape Communications, went
public in 1995, and brought with it a new economic model based on gaining market
positioning and becoming the technological standard at the expense of huge loses up
front. Its' stock returns during its first two years were in the hundreds of percent and it
quickly commanded valuations that analysts were hard pressed to justify. In fact the
company was enjoying the benefits of a market that -despite its somewhat irrational
assumptions- was pricing it as a pure growth option with a potentially very high payoff.
Many other companies followed.
But as said before we need not look to the last decade for such kind of valuations.
In 1901 papers were talking of a "new era" as new technologies and business models
were adopted by the economy, high tech new companies and consolidated old ones
dominated, and the S&P 500 achieved a local price earnings (P/E) ratio peak of 25. The
same happened in 1929, and later the decades of the 50s and 60s brought again economic
optimism and high valuations. Thus the "new economy" and the firms that dominate it
are only new in a temporary sense. That does not mean that the new economy is not real,
just that we must understand what we mean by it.
4.1.1 What we mean by New Economy Companies
We know a new economy company when we see one. It often has had a short life
-may be a new IPO or even still venture funded- or has experienced some sort of
corporate rebirth -often through acquisitions, divestures, spin-offs or sales- from an old
company. It is often small but even if it is not it always is fast growing in revenues and sometimes- earnings. It commands hard to justify multiples. And it often is the center of
media and analysts attention due to its new technologies, marketing strategies or
manufacturing processes. In the 1990's companies in the technology fields dominated the
4-41
new economy ranks, but with the wide adoption of the Internet telecommunication and
media companies that were essential to its functioning and benefits joined what was
understood as the new economy. But as we have seen the new economy companies of
the 1990's were not those of earlier periods, and will almost certainly not be those of
future ones either. So what is it that makes a company a new economy company?
Characteristics of the Old and New Economies
* New Economy
Old Economy 4
Companies mostly are...
* Startups
Mature Firms 4
Cash Cows 4
Value mostly in...
0 Growth Opportunities
Multiples are...
Low
o High
4
Figure 4-2: The old and new economies compared.
New economy companies are those whose value is dominated from growth
opportunities. As we have seen before growth opportunities generally accrue from the
uncertain benefits of today's investments on the future cash flows of the company. That
is, new economy companies originate from highly uncertainty but potentially highly
profitable investments of the sort that gave rise to the need for real options theory. Those
for which the payoffs could take any number of very different values and for which
managerial decision making is crucial to maximizing the worth of the firm. Owning
opportunities for growth is the result of the projects the company management has
decided to undertake. And as we know most opportunities for growth do not have an
infinite lifetime. Thus being a new economy company is not something that is inherent to
the firm, nor is entering a new economy something that is a one-time event. It is a state of
companies and the economy to which they belong and both companies and the economy
can enter and exit new economy phases in their development. Companies are new
economy when on the whole they are dominated by growth projects, and the economy is
only new when on the whole such companies dominate it. As these projects exit the
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growth the phase, which they will by the invariable laws of economics, they will revert to
old economy and unless the firms that own them engage in new growth ones the firms as
whole will also revert to old status and the economy as a whole will follow suite. We will
now proceed to explain more carefully how to determine the new versus old economy
status of a firm.
4.1.2 Projects and Project Portfolios
Much of valuation centers on the decision making process of whether to invest in
a promising project or not. Real options theory was developed as a method of project
valuation, and net present value in fact refers to a method of evaluating projects.
Discounted cash flow valuation is an NPV inspired method of pricing the equity of firms.
This is fine because in essence firms are portfolios of projects. We can observe this from
the fact that some companies are in essence a single project. Often companies get started
for the sole purpose of developing and operating a single property, as is the often the case
with national infrastructure. Technology startups themselves begin in order to develop a
single product or service and market it to consumers or corporations. These startups as
they mature add more product lines becoming multi-project companies. On the other end
of the spectrum are conglomerates, which are clearly multi-project companies. While
conglomerates where in vogue for some decades in the 20t century, it later became
apparent that agglomerating very disparate interests did not increase value to
shareholders and therefore many undertook a process of project divesture that
concentrated the divided entities in certain lines of business.
The implication of this portfolio view of companies is that the some of the
consequences of Markowitz portfolio theory hold true not only for financial portfolios but
for companies too. The value of companies is simply the sum of the value of its projects
when proper care is taken to avoid double and under accounting, the expected return is
simply the weighted average of the individual returns of the projects, while the company
risk can be found by summing up the entries of the projects' variance covariance matrix.
Further implications is that companies should not be worth more than the sum of their
parts unless there are truly some synergies in the merged entity, but that nevertheless a
company can reduce the volatility of its expected return by properly diversifying its
sources of revenue. Nevertheless it is not clear that shareholders are willing to pay extra
4-43
for this diversification that they could achieve at a lower cost themselves directly
investing in the financial markets.
Company Value =
(CashFlowProjects)+ E (GrowthProjects)
PortfolioReturn=wa * ra + w
PortfolioVariance=
*
a
rb
wa2
+(2*aw*w*p*cr*
*
Pat
)
Equation 4-1: The value of companies is the sum of the value of its individual cash flow and growth
projects. The second and third equations give the portfolio return and variance given expected
return and variance of the portfolio's two constituent projects.
A realization of greater significance than this is that not all projects are similar in
characteristics and that not all projects are valued by the same methods. Older more
deterministic ones are better modeled as a steady stream of cash flows while newer more
uncertain ones are better modeled as options for growth. In particular all those businesses
that provide cash from operations that grow at a constant rate into the future and that
require relatively little investment -or cash cow businesses- are of the first variety, while
R&D projects, marketing investments and other kind of uncertain investments with
uncertainty payoffs are often the second. The key is to recognize which is which.
Old economy companies as we have described in the previous section will have
most or all of their value concentrated in cash flow projects, while new economy ones
will have most of their value in growth ones or evenly distributed in a mixture of both.
Contrast this with debt and derivatives. Debt traditionally has certain payoffs whose
value is straightforwardly calculated from discounted cash flow methods. Derivatives on
the other hand are more complex, but equally as pure, instruments that can easily be
priced by summing up the value of all the options that constitute them. The issue with
new economy equity is that it is not based on clearly certain events or on clearly
uncertain ones but rather has elements of both and therefore a dual thinking must be
necessary: company equity contains both certain cash flows and uncertain payoffs from
options, rather like derivatives contain a sum of uncertain payoffs.
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Debt,
Old Economy Equity
New Economy
Equity
Portfolios of...
Options
Cash Flows
Value with...
Net Present Value,
Option Pricing Theory
Discounted Cash Flow
Figure 4-3: The uses of net present value and options pricing theory.
From a practical valuation point of view one of the issues we must carefully
encounter is how to separate the cash flows and investments of companies into individual
lines of business. In some cases, like when we are valuing startups, we may be valuing in
effect a single project company and thus it is easy to assign the cash flows. In some
others, like is often the case on the entire cash-flow stage portfolio of companies,
separation adds little information at too much cost and is therefore not necessary. Thus in
general separation makes most sense in the case of individual growth projects, or even an
entire portfolio of them -like when valuing an R&D lab-, and often in those cases
companies make some special information available to the public thus facilitating value
separation.
4.1.3 Project Life-Cycle and Portfolio Analysis
As we have seen above projects are operations that enterprises undertake and that
mature over time. Because the valuation multiples that a project, and the company it
forms part of, are influenced by the project's stage in life, an analysis of the company's
projects lifecycle is an integral part of the valuation process. New economy projects
typically begin their life in the R&D lab of an established company or as the only idea
that a research or prototype stage startup has. This is typically the stage that represents
the creation -or purchase- of the first option for growth in a compound/learning option.
At this stage some of the value is recognized, but often the risks are so high that this
value does not usually translate into much capitalization. As the technology matures the
4-45
product or service goes from R&D, to engineering design, to manufacturing design and
each stage representing the exercise of an expiring option and the creation of a new
option with greater and greater value.
Once all the technology phase of the project is over and it begins shipping it
usually goes through several market expansion options, as new customers are added to
the line. Traditional means of doing this is when the product or service is marketed to a
new industry, to a new country, or whichever of the personal, small, mid or big business,
or institutional sector it had not previously been marketed to. Moreover often products
serve as platforms of other products. Thus when Microsoft introduced Windows 3.0 it
was creating the option to grow the operating system into wide family of operating
environments. Nevertheless eventually all options must take a path to cash flow, at first a
rapidly growing one and later a more mature one. At this stage the method of valuation
changes as real options becomes less appropriate than discounted cash flow.
Investors
Inves(Dividends
Growth
Opportunity
Excercise
C
Ines
Divest
Invest
Cash & Eqv.
Figure 4-4: The life cycle of new economy funds.
The flow of funds in the new economy begins when investors originally purchase
the equity of companies that have nothing but project ideas. These investors are in fact
capitalist entrepreneurs who take very large risks for the promise of uncertain but
potentially very large payoffs. Thus these investors in fact purchase growth options.
These new economy companies research and develop products and services that may turn
out to be profitable when sold to their customers. When this happens the project matures
and become a cash flow project -at least in part since further customers and derivative
products can be gained from it. Eventually however the project matures completely but
4-46
probably by then the company will have used the proceeds from cash flow to invest in
new growth options. If the haven't they could use the cash flow to pay dividends to their
stockholders and truly become and old economy company. If they have they will need to
keep investing back the proceeds from the new projects themselves as they mature to
sustain their existence as growing entities. Another alternative is to sell the cash flows
and use the proceeds to purchase new growth options and sustain their high valuation..
Any individual company can move its projects from old to new economy back
and forth by means of skillful management. Coming went from an old economy glass
manufacturer to leading supplier of fiber optic cable for the bandwidth explosion. It shed
many of its old units and used the proceeds to acquire growth options. Cisco System's
skillful maintenance on the top league of growth companies has rested on its ability to
use its steady stream of cash flows to finance the acquisitions of new growth options.
These options it exercises and uses their cash flows to finance more acquisitions. PC
manufacturers like Dell on the other hand have experienced an exercising of their options
with no meaningful new ones being acquired, and hence a fall in their relative valuations.
It is arguable that eventually scale presents a problem to any company, as options large
enough to surpass the value of the steady stream of cash flows become scarce.
This is difficulty in trying to maintain a position as a new economy company is
compounded by the fact because most options have a finite life. Nevertheless there are a
few options that do conserve their value close to forever, as long as skillful management
keeps them active. Very strong brands are some of these, as companies like Disney can
use their name to facilitate the introduction of many new media content products. The
investments the company continuously makes on the Disney name ensure that the option
-or a portfolio of options that resemble a single perennial one- always exists, and that
only incremental investment is needed on individual products to create consumer
awareness.
4.2 Understand the Company: What does it do?
Now that we've explained the basic principles necessary to understand new
economy companies' valuation from a real options perspective we must learn how to
implement the method. The first step in such process is to understand the company, what
role it plays in the economy, its history and its intended future.
4-47
4.2.1 What lines of businesses is it engaged in?
The first step in valuing a new economy company is determining in what lines of
business the company is engaged in. First we determine if it is a product, a service or a
combination company. If it has products we determine if there are hardware, software, or
technology -ideas such as patent rights- products or some combination of them. If
services we determine if it has consulting services, utility like services (such as providing
communication lines), or others. No less important is the fact that we must determine if
the company is primarily a manufacturer, a marketer or an R&D lab, among other
possibilities. This last distinction is of crucial significance because on it will be based the
focus we will later grant its various productive assets. Even in the case that the company
is primarily a hardware product manufacturer for example we have to clearly determine
what products does it sell.
Thus for example if we were to define the business of Dell Computer we will
have to specify it is a personal computer manufacturer and marketer, with presence in the
desktop, laptop, server, workstation and storage markets. In other words we will have to
specify its segment information. Companies' annual reports, 10-K forms, and IPO
prospectus are the first source of this information, but many other sources are available.
Fundamentally the question we are trying to ask is: "What projects does the company
engage in?" That is, we are trying to determine the composition of its project portfolio as
it stands today.
4.2.2 How did it get there?
After we have determined the company's project portfolio we must determine
what path did the company take to reach its current state. In other words we must
determine its historical project evolution. If the company has been established for many
years chances are this path is long and complicated, but as we have seen above this
company will most likely be an old economy company and therefore this kind of analysis
will probably supply less useful information, will thus be less necessary and therefore can
be done in less detail. Most high tech companies that we know today are at most two
decades old (from the beginning of the PC boom), and many are younger than five years
(the Internet's commercial birth). Among exceptions one notorious one is IBM, but many
of the ongoing projects of this company are clearly in cash flow stage, although
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nevertheless it has plenty of growth opportunities in its labs. The primary value of this
kind of historical analysis is that it allows us to determine in what stage are the
company's projects -which we determined previously- currently in, and it gives us hints
as to where does the management of the company intend it to go next.
Going back to our Dell Computer example the company was founded as a desktop
PC manufacturer, but later used its options for growth to enter the notebook, server and
workstation markets and later the storage market. It has most of the time remained a
direct seller, but after being a direct telephone and face-to-face marketer it added the
World Wide Web as a channel. It also originated as a US company that first expanded to
the UK, and continued adding served countries as it matured with most of its efforts
centering this days on the Asian growth markets: China, and South East Asia.
4.2.3 Where does is it intend to go?
The most important reason why we need to know how did it evolve into its
present day form is to be able to determine where it may go in the future. It is in the
future of the company that most of its value is present, especially if it is a new economy
company. Most of the value will be in the form of growth options for which we must
determine what is their objective (what cash flow do they intend to secure), and how
(what is the uncertain factor that must be determined) and by when will this objective be
obtained. We'll discuss the last two more carefully in the next sections.
Management plans and strategies are the most important source of future growth
opportunities for companies. In general it is the company executives who must be open
to, and even pursue the opportunities that the market will present them. In this sense it is
much about vision. Nobody, not even the company's management, knows what the future
will bring, but the management must be able to see that unexploited opportunities exists,
must position the company to take advantage of these opportunities, and must execute
their strategy when the future clarifies there are profits to me made from them. In other
words, management must engage in real options thinking. It is therefore valuators job to
enter management's minds and build this options strategy into the model. This task can
be facilitated by disclosure and communication, but can also be derived by modeling
management's strategic thinking from economic principles and the company's style.
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As a matter of example it is known thus that many PC and server manufacturers,
such as Dell, Sun Microsystems and Compaq, are aggressively pursuing the storage
market. They already own markets shares from which they derive cash flows, but
doubtlessly in their minds most of their value in the segment rests on the options for
further penetration. EMC Corp., the actual leader in the field with a 35% market share, is
in fact pursuing its own growth strategy by emphasizing its storage management software
products. In a different field Internet portal Yahoo! Inc. has recently commenced a
strategy of diversifying its revenue stream away from advertising by charging fees for its
online sales and auctions, and may soon add other services to its revenue generating pool.
It was in fact these options that gave Yahoo! its large market capitalization -which toped
$ 100 billion-, before investors' change of perception of the company's future cut it down
to a more modest $25 billion today.
4.2.4 What does/did the path depend on?
Once we have determined the objectives the company is pursuing we must
identify on what event outside of the control of the company -or partially under its
control- do the attainment of these objectives dependent on. Often these events are the
presence of certain market conditions, which in a practical sense mean the existence of
demand. Nevertheless
this demand is often dependent on the penetration of
complementary products or services, the purchasing power of the customers, and other
factors that we must determine. Building all of these into the options model would be a
hassle, and would result in rainbow options that would not be easy to value. Therefore we
model their effects by stating that a certain potential demand or revenue S. may
materialize for which the option has a certain payoff Cu, and that the demand Su is the
result of all the conditions that we have determined.
As an example of this we notice that Yahoo! Inc., the leading Web portal
company, would not have achieved its status had Netscape Communications (now part of
AOL) not developed and popularized Web browsing technology, had AOL and other
Internet service providers not popularized connections to the World Wide Web, and had
US Robotics (now part of 3Com) and other modem companies not delivered connection
speeds of at least 56Kbits/sec to most households, to a name a few.
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4.2.5 When do/did those events happen?
Just as it is important to determine what impacts management's decision to pursue
certain paths it is important to determine when the decision itself is taken. In the world of
real options there is not hard expiry date, as it is the case in financial options, but
nevertheless there is a relatively fixed length period of time over which financial markets
revalue companies
opportunities.
Thus
if they determine that said companies have missed growth
an approximate
expiration date does
exist. We use this
approximation, which we derive from study and educated assumptions, to put a precise
date on the expiration of real options, but we must recognize that these dates are flexible.
All possibilities have to be analyzed and the most likely one chosen but allowed margins
of error of several months -about a quarter is right-, and nevertheless we must
continuously assess our model as the future plays out.
Suppose that Juniper Networks is developing a new high-end router for the
Internet backbone service provider market. Juniper has determined it will require two
years to arrive at a commercial product from its current research prototype, and that at the
end of those two years it may be able to sell the product at a profit. Nevertheless the
company also knows that Cisco Systems is developing a competing router and that if its
own is not available in at most two and a half years then Cisco's will be, and it will
conquer the niche. Thus there are two companies competing for the same cash flow and
only the one that exercises first its growth option will be able to secure the profits. Thus
the true expiration date of each option is the exercise date of the other option, which will
probably be no earlier than in two years and no later than in two and a half. Nevertheless
if neither company exercises, both options may well expire worthless since in four years
both products would have been rendered obsolete. Also, if a new paradigm renders both
products obsolete before the two years, it would imply that the true expiration date has
been foreshortened further.
4.2.6 Sketch an evolutionary tree for the company
An evolutionary tree summarizes all the information and insight we have
developed over our study. Depending on how old a company is we may begin the tree
with incorporation and/or the initial public offering, carefully analyzing what was the
company trying to achieve at the outset and whether it is still pursuing the same goals.
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We should include information on product launches, advances on research projects,
customer acquisitions, corporate acquisitions and divestures and other company events
that have the power to impact value by determining the outcome of option events,
creating options, divesting options, or acquiring or selling cash flows. An evolutionary
tree should flow in time but it is not necessary that it should be so precise so as to prevent
some overlaps in the time axis where they are imprecise. An evolutionary tree can also
serve to emphasize the relative importance of various projects by making some more
clearly visible or central than others. Of importance in drawing an evolutionary tree is
recognizing that the company may have reinvented itself entirely along the way by
shedding most of its old units and acquiring plenty of new ones. As discussed before, this
has been the case of several large technology companies such as Coming and EMC Corp.
December 1999.
M20
Internet
Verio
router
Decem ber 1997.
e.Ss
JN SO
1996.
Inc. February
R&D commences.
September 1998.
cable and
M40 Internet router
W ireless
IBM
Solectron
manufacturing
agreem.
manufacturing
agreem.
UUNET
axis
Figure 4-5: Juniper Networks evolutionary tree from inception to December 31, 1999. Product
launches have been assigned to boxes, Semiconductor and board manufacturing agreements have
been assigned to the time axis and customer acquisitions come after the products they have
purchased. Significant corporate events, such as the company's initial public offering, are also
included.
Above we include one example of an evolutionary tree. Juniper Networks is a
young company and therefore its history is simple. Nevertheless by drawing its diagram
we intuitively arrive at some of the assumptions that will allows us to do the real options
valuation. We can see how many customers it has and when did it gain them. We see
what products lines it has to offer and how it may expand them. We also recognize that
like many young electronic developers and marketers Juniper out-sources most of its
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manufacturing. We can foresee that Juniper will incur low fixed costs of goods sold and
a variable cost of sold that is proportionate to volume. We can guess which customers it
will acquire, or which customer that it already does business with will buy a new product,
and other such insight and information.
4.3 Structure the Problem
Use the Binomial and Discounted Cash Flow Methods
In the first part of the solution process we concentrated in understanding the
portfolio structure of the company. We determined in what projects is the company
currently engaged in, and whether those are cash flow projects or option projects. The
next step is to value each project separately according to its type.
For cash flow projects we should use traditional discounted cash flow/NPV
methods. Thus we must make projections for cash inflows and outflows several years into
the future, we must estimate the cost of capital associated with the projects using CAPM,
the three factor model or some other suitable alternative and we must discount back to the
present the value of the project. It is outside the scope of this paper to give a detailed
description of this process. Nevertheless the process must be carried out carefully
especially to ensure that there is no double or under accounting of revenues or expenses
in the whole company valuation. A way to guarantee this condition is to base the whole
valuation on a DCF model and only add option values to account for special investment
projects that would otherwise simply be expensed. Alternatively option values can be
computed as the centerpiece of the valuation model and DCF analysis can be added to
round up all parameters that have been left out. Below is a more detailed description on
how to value the option parts of the company.
4.3.1 Model the Uncertainty: Draw an Event Tree
By analyzing the company we derived an evolutionary tree that charts in broad
terms the progress of all individual projects over their lifetime. Now we must extract
from this evolutionary tree that focuses on the whole company the knowledge and
assumptions that pertains to each individual project and round out in greater detail the
market information that is necessary to have completed event trees. To achieve this result
we go back to the first question we asked when setting up the problem, and ask again if
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these lines of business correspond to actual distinct projects, and if so we search for the
answer to the third question to see if these distinct projects are best modeled by options or
cash flows. If they are modeled by options then it is best to draw event trees for them.
The necessary additional information can be found by looking at the answers of
succeeding questions such as what does the event depend on, and by when is the
resolution expected.
What we really seek are demand numbers that will indicate the maximum
potential revenues the company may enjoy. How to arrive at these demand numbers, and
what is relevant to them is something that is very company specific, but in most cases can
be though of as a simple multiple of the number of goods that can be sold, and the price
for which they can be sold, not unlike the top line of a forecast income statement. This is
the constructive approach -that which begins by the smallest unit and builds up. Another
way to arrive at the demand numbers is to determine what could be the total market size
of the product and extracting the fraction of the market that the company hopes to secure.
Moreover both approaches are compatible because we may have determined the total
market size through a forecast of total number of units multiplied by an average selling
price.
In particular cases we can arrive at such demand estimates quite easily by looking
for the costs up the supply chain. Thus for example research studies concentrating on
consumer purchases of cellular handsets give us the total market size that a company in
the industry, such as Nokia, will encounter. Similarly a company that sells power
amplifiers to Nokia and other handset manufacturers, such as RF Micro Devices, can
derive their total market size by taking the fraction of handset makers' costs of goods
sold that corresponds to their products. Many other sources of forecast market
information exist -especially in the highest growth areas such as wireless and storagethat can be consulted for estimates.
In general determination of these numbers is not unlike the determination of
revenues in a DCF model. Nevertheless there is one important difference with respect to
DCF models; while in DCF models we seek to estimate the single most likely outcome of
events, in real options event trees we seek to establish at least two but possibly more
probable outcomes. How do we determine these alternate values? Like in DCF models
4-54
one approach is to assume a proxy high rate of growth path and a proxy low rate of
growth -or even contraction- based on percentages. We could assume that in a one period
growth option project the revenues may grow either 100% or 50%, each representing one
path of the event tree. These numbers in fact may not represent the actual most likely
path, which may be in between both -say 70% growth- but there rests the key. Our
thoughts must be reoriented from the most likely event -the median- to two or more
events that weighted by their probabilities will give the expected outcome -the mean.
4.3.2 Model Managerial Flexibility: Draw a Decision Tree
Once we have determined and described the sources of market uncertainty we
must also determine and describe what would be the optimal decisions management will
take in each uncertainty resolution state. In essence the process consists of determining
what will the payoff to the company be if the management exercise or not at each point
and choosing the most profitable -or least costly- alternative. For this we must know the
strike price -or fixed costs- of the option, the marginal costs -which can be modeled in a
fashion similar to fractional ownership- and any other possible peculiarity the payoff
diagram may have in each situation. In subchapter 3.2 we showed the basic payoff
structure of a long call and other option positions, but although this model may have the
virtues of simplicity without loosing focus on the two main traits of any payoff -a fixed
and a variable cost- any forced application of this exact model may result in results that
are not meaningful. Thus we must always apply models with our particular problem in
mind.
For example, we may have a company that may have product for which it is
responsible from a design and marketing point of view, but which it may not manufacture
internally for competitive reasons. Many electronic circuits and devices startup
companies will often fall in this category, since they may not have the resources to build
and maintain large expensive printed board or semiconductor plants. Thus the company
will probably choose to subcontract the manufacturing to an electronic manufacturing
service company such as Solectron Corp. or Jabil Circuit, or perhaps a large hardware
company with spare capacity such IBM. But such a subcontractor will charge its services
in a fashion that is likely to benefit large orders over small orders, probably charging less
per unit for large orders. As an example, semiconductor manufacturers charge original
4-55
equipment manufacturers less for orders over 1,000 units. Thus kinks could be introduced
in the payoff function, increasing the number of pieces in the diagram from two to
potentially many more. And this information is needed in order to determine the payoff
instances of each leave in the decision tree.
Once we have the event tree and the payoff diagram we can proceed to combine
the information contained in the two to determine the right managerial decision and the
benefits that such a decision will accrue to the company. In the case where we had two
terminal leaves in a one period tree we must find the market point of each terminal event
in the payoff diagram on the stock axis, read all the information pertaining fixed costs,
variable costs and any special items, and then write down the payoff as determined in
each leaf on the decision tree.
4.3.3 Estimating the Real Options Payoff
One of the issues of doing real option valuation is that we must be careful to deal
with cash numbers. When we value financial options we deal with cash investments, cash
strike prices and cash payoffs necessary for or resulting from the position. Nevertheless
much of the data that we have available for estimating the value of real options comes
from company financial statements, which are prepared to comply with standard accrual
accounting rules such as those outlined by the FASB in the Generally Accepted Financial
Principles (GAAP). These indicate that accrual devices such as depreciation, amortization
and depletion are to be used to spread capital expenditures over the revenue period, that
research and development and sales and marketing costs are to be expensed as incurred,
and that in general capital expenditures are treated should be treated as expenses to be
accrued in a period that matches the revenues they generate, or that they are to be
expensed immediately if the revenue is uncertain.
This makes sense for accounting purposes but it does not for real options
valuation. First because real options valuation, just like NPV, must be cash based: the
cost of items must be recorded when they are paid, which may or may not be when they
match the revenues they generates. But perhaps most importantly because these costs are
not really seen as expenses to be distributed over time, but as one off investments that
may result in increased revenues in the future. This is the foundation of real options
theory. While in GAAP based DCF valuations we seek to compute net income by
4-56
expensing all costs that are to result in uncertain payoffs as they are incurred, in real
options we seek to see such cost as investments on real options that may provide benefits
or not.
4.3.3.1 How to Account Depreciation, Amortization and Depletion
Whenever a company is involved in the purchase of a new manufacturing plant, it
is generally committed to pay for each stage as its contractors complete it. Nevertheless
for accounting purposes generally the same plant will be expensed over its useful life,
which does not coincide with its completion, and could last several decades. If we are to
do a real options model of a planned plant expansion we must avoid the GAAP approach
to capital expenditure and use a completion approach instead.
Typically a company that commissions new infrastructure will pay for the project
in installments. The first of these may well be options to actually pursue the building of
the plant, or if not may be down payments for initiation of the project. Whatever they
may be the first round of payments will in fact represent the price paid to purchase the
option to build the plant. Subsequent payments will in turn represent the exercise of the
option or the chain of compound options. Each of these payments should be expensed
immediately, in the sense that they should be interpreted as one off investments. The
payoffs will appear at each exercise as they occur and thus will in a sense be expensed
immediately too. They key is that cash transactions are matched through the execution of
the entire option rather than by revenue and expense matching.
4.3.3.2 How to Account Operating Expenses
Research and development, sales and marketing and other traditionally recurring
expenses in accounting statements most also be rethought in light of the real options
approach to valuation. One of the observations that led to the development of real option
theory was that R&D investments, which are highly uncertain in their payoff, must often
be expensed without being able to properly forecast or measure the benefits that the
investments will accrue. It was also observed that this approach underestimates the value
of these investments to the firm. Thus it was observed that the GAAP approach to this
kind of expensing and its impact on perceived company value, as well NPV's own
difficulties, were among the leading indicators of the need for a real options approach to
uncertain investments.
4-57
In a real options framework we seek to establish such expenses as investments in
the future growth of the company. R&D projects, engineering design, and other
accumulation of technical know how become option purchase -or creation- operations
whenever they can be properly identified with a potential payoff no matter how unlikely.
Similarly marketing and some sales cost, which result in potentially increased future
benefits due to brand awareness, distribution networks, or market positioning must also
been seen as options for growth.
To see why this approach to uncertain but nevertheless capital building
investments is justified we need not see further than the way startup technology
companies allocate their resources during their early stages of development. Often these
companies commit substantial resources to building their organizations, particularly their
product portfolio, sales organizations and their administrative bureaucracy. Sycamore
Networks a marketer of optical networks products spent more than their revenues during
their first full fiscal year (1999) on operating expenses. The company had revenues of
$11 million, out of which $8 million represented the cost of revenues. This allowed them
to earn a gross profit of about $3 million. Nevertheless they incurred expenses of $14
million in R&D, $4 million in sales and marketing, and $1.5 million in general and
administrative, clearly sending their net income negative. The reason Sycamore operated
in such a fashion was because such expenses represented a building of non tangible
assets: technical, sales and administrative know how that have value. But these assets are
in fact larger than what a company of Sycamore's current size based on its revenues
needs. Thus in effect these expenses represent investments that will allow the company to
pursue increased cash flows in the future. In a real options framework these costs will
indeed be expensed immediately but the difference is that it will be stated that they
represent the purchase of an option to certain cash flows in the future, as it should be.
With this new view on operating expenses it will possible to value early stages
startups more accurately, and see none COGS expenses for what they are: investments
necessary to earn cash flows on the companies' products. This does not mean that all
operating expenses now become investments, since many will accrue no benefit. But it
does mean that we should look carefully to what is behind them and especially in the case
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where they seemingly overwhelm the gross profit look out if these expenses represent
actual commitments to future growth on the part of the management.
4.3.4 Compute and Understand the Real Option Value
Once we have arrived at a decision tree in the binomial solution process the next
step is to set up a portfolio composed of some cash flow and bonds that replicates the
desired payoff. This step is mostly mechanic but can be tricky if we are not careful.
Generally we will use the revenues of the company as the cash flow itself, just as we use
the underlying common stock when we value equity options. After all the only security
that will change together with the payoff in the exact same states of the world is the
project revenue. Our bonds will simply be dollar value securities that pay the risk free
rate of interest on whatever time basis our option uses, which most of the time will be
yearly.
Below are equations for the value of a call. These equations are equivalent to the
binomial equations in chapter 3, but have been solved to specify the value of a call in a
single mathematical expression -without recourse to intermediate values such as the
number of stocks or bonds in the portfolio- as a function of our replicating portfolio
parameters.
C C=
SU
C= S-
u
Cd
Su
USd
(1+ r)
*S+
-Sd
(1 +r)
u
*Cu
"
+
SU -Sd
(1
r
Equation 4-2: Equations for the value of a one period binomial call option given a replicating
portfolio with underlying stock S and risk free rate r. The second equation allows altering the value
of the option as a function of the current stock price S, the values of the stock and call in case of up
and down movements (Su
Sd Cu Cd),
and the risk free rate r.
By observing these equations we realize that the value of a call option is directly
proportional to the value of the underlying cash flow and its own payoff in the case of an
upward movement of the stock. Less clearly seen from the equations is that the value of
the call increases with the value of its downward movement payoff. This can understood
intuitively however because in either case when one of the payoff rises and the other
remains constant the call can be worth no less: it just increases our expected payoff no
4-59
matter what the outcome is. As either the value of the stock up or stock down parameters
increase the value of the option falls however. Mathematically this is so because less of
the stock will be needed to replicate the option payoff.
-NStck
-4 Stoxck Up
Dw
60
S
Call Upw
50--
45
35
-20%
-10%
0%
10%
20%
Percent Change
Figure 4-6: Percent change in value of a call as described by the equations above for any given
percent change in its stock, stock-up, stock-down, call-up, and call-down parameters. The original
parameters in this example are $100, 200, 50, 100, and 25 respectively. Notice that the current value
of the stock has the greatest impact, but that the change in the upward payoff is the second greatest.
Above we have a chart of the change of value of an option relative to a change in
value in each of its parameters based on the call equations at the beginning of this
section. Our example describes a situation where the cash flow is currently worth $100,
may halve or double in value over one time period, and where the payoff from the call
will be 50% of the revenues in either outcome. We notice, as expected, that the present
value of the stock has the greatest impact on the price of the call. Other than the risk free
rate of interest -which is not plotted- the changes in either the stock down or the payoff
down parameters have the least impact. This is so because they are worth the smaller part
of the option. Remember that the option is valuable because it allows us to profit from the
upside without loosing out on the downside. In this example we have a situation were in
essence we have two strikes that allow us to profit from two outcomes. And the lesser
one is the one that is responsible for the less value. Nevertheless one general lesson to be
taken from this example is that sensitivity analysis -using with charts like the one above-
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on our parameters is crucial to understanding what real option values inform and how are
they impacted by different assumptions.
Now lets make some simplifying assumptions to the equations. Assume that the
call is worthless in the case that the price of the underlying asset or revenue decreases.
This allows us to eliminate the value of the call in the case of a stock fall. If we then go
back to the statement that the value of a call is a function of the value of the underlying
asset, and in particular enforce that its value is equal to the gross margin we can extract
from the cash flow minus the strike price of the call, where both the margin and the strike
price are known parameters, then we simplify the equation further because we have
eliminated the value of the call in the case of a rise in the underlying cash flow. Thus all
we need to determine are possible values for the underlying cash flow in the future, the
possibly value of the fixed costs to be exercised and to look up the risk free interest rate.
This problem in fact has almost been reduced to the level of complexity of a standard
discounted cash flow problem, but with the advantage that we deal with capital
investments and gross margins in a real options context.
C= S-
"
(1+ r))(
Margin*S-K + Margin*S, - K
SU-Sd
(1 + r)
Equation 4-3: This is the same as the second equation 4-2 with the value of the call equal to zero in
the down scenario and equal to the (gross) margin times the stock up minus the strike in the case of
an up scenario. This situation is probably the single most common for all real option values.
In the figure below we show the value of the call described by the equation above
when we let the variable and fixed costs vary. This has important implications as it
explains why two companies -for example a hardware and a software one- which have
identical underlying cash flows but different payoffs show different multiples in the
marketplace. Such could be the case of Microsoft and Intel, as we have described in
previous sections.
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70-
60
.
-
0 60.00-70.00
5000-6000
50-
0 40.00-50.00
1330.00-40.00
40-
0320.00-30.00
Value
S10.00-20.00
00.00-10.00
20
10
0
20
**60
0y
2030%
Variable Cost
40%
80
60%
Fbxed Cost
100
Figure 4-7: Value of a call as we vary the fixed "K" and variables cost "(1-Margin)" in the equations
above. The other parameters are stock up at 200, stock at 100, stock down at 50, and the risk free
rate at 5%.
For mathematical completeness we can now transform the last equation to include
the up "'u" and down "d" parameters or the volatility parameter "a" that we use in the
context of financial options, and rewrite the equations below. From these equations it
would be possible to derive a chart that plots the call value C as a function of volatility.
Nevertheless the volatility parameter and its proxies are rarely used directly in company
valuation because by basing ourselves in volatility we constrain our freedom in
determining stock changes and payoffs flexibly. Moreover for financial options a price
versus volatility chart is available in many options textbooks. From these equations it is
just important to undertsand that price is a positive function of volatility, as we have said
before.
u*S
(1+ r)
Margin*(u*S)-K
(u -d)* S
eC*S*
(I+ r)
Margin*(e"*S)-K
(e' - e-)*S
Margin*(u*S)-K
(1+ r)
Margin*(e*S)-K
(1+ r)
Equation 4-4: Equations relating the value of a call to the value the underlying cash flow given an
upwards movement of "u" and a downwards movement "d", or a symmetrical upward and
downwards movement with volatility "a". Notice call value increases with volatility, margin and
current cash flow value while it decreases with strike price. This is a one period option.
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One other particular context of importance in binomial valuation is compound
options. This type of options are one of the most frequently used in valuing new economy
companies because all company projects are in a sense the outcome of previous projects.
Knowledge has accumulated and this knowledge has acted as invested capital in the
pursuit of new projects. What we must guard from when dealing with compound options
is that the value deriving from imbedded options must be included in the payoff of the
first one. That is, the prices of successive options are included with the cash flow minus
the strike at the terminal period of the first option. Second we must ensure that the
present value of the stock at period zero includes the cash flow derived from successive
periods. But this would be the case if we have derived our event tree properly. Finally the
value of the stock has to match at the instant where both options exist. That is elementary
bookkeeping.
4.4 Sum the Values and Analyze the Company
Once we have computed and analyzed the value of each individual project we
must study the value of the company as a whole, as we study a portfolio of equities or
cash flows. One key distinction we must quickly make is what is the aggregate value of
option and cash flow projects relative to each other to understand whether the company
truly is a new or old economy one. Any company whose value is more than 50% derived
from growth opportunities probably deserves to be called new economy whatever its
industry is. Looking at the aggregate option versus cash flow values also serves to
visualize how much of the capitalization is at risk in case of an unfavorable turn of events
in the future. It also serves to explain valuation multiples as a company consistent of
mostly growth options will not have the cash flows to justify its valuation on that basis.
Also we should know if one single project, or a small group of project, account for most
of the value whatever they might be. We could further see if the company's options for
growth derive from developments in its R&D labs, or from the potential to acquire new
customers. Pie charts will generally allow us to intuitively understand percentages while
mounted bar charts will allow us to grasp absolute values in addition to relative ones.
Other visualization aids should be used to emphasize further important points.
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4.5 Review and Redesign if Necessary
4.5.1 Compare the Real Options Value with a DCF One
Comparing the real option value we have computed with the value given by the
discounted cash flow method is more than just a mechanism to check the integrity of our
model, it is also a way of determining the option content of the company. It is because of
the potential to shed light on both of these issues that we often do a DCF model and
compute its value to complement our real options model. One way to go ahead is to
collapse the real options model into a DCF one. We probably already have a set of
projects being valued by the NPV method. Thus it rests just to collapse the option
projects into NPV ones, by assuming certainty in the outcomes and no managerial
flexibility, and adding all of their values. This of course defeats the point of why we
valued these projects via the real options method in the first place: because they were
project with considerable future uncertainty. But we must always remember that if we
choose to do this DCF check it is just to shed some further led into the company and our
valuation methodology and not because we believe it is the better method.
4.5.2 Compare the Computed Values with the Market Capitalization
One of the key methods to determine if our valuation process has been successful
is to compare our result to what the financial markets believe the company should be
worth. By comparing our computed value with the market capitalization we should be
able to assess within a reasonable discrepancy if we have included all relevant factors and
if our assumptions have been reasonable. It is unlikely that the market will be terribly
wrong in its assessment; although it may well be that this is the case. In fact we may be
trying to prove that the market is mispricing the company, in which case we are by
definition doubting our check, nevertheless the comparison can always shed important
criticism.
Except in the case of believed extreme market mispricing our computed value
should certainly not be discrepant from the market value by more than an order of
magnitude, and more stringently by more than 50%. In particular we should ask ourselves
if we have made too optimistic or pessimistic assumptions, or more fundamentally if our
model is faulty, should we notice that our result gives too large or small a value relative
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to the market. Is there anything that the market knows that we don't? Is there anything we
know that the market does not? Is the market currently gripped by short-term panic or
euphoria? All of these are important review questions.
We can increase the reliability of this assessment by looking at other companies
in the same industry as the one we are currently analyzing and also by looking at the
same company at a different period of time. The first comparison will allow us to see if
the general sentiment relative to this particular company is good or bad relative to its
competitors, and if so we must determine why. It may indicate an expectation that the
company will take or loose the market lead in fashion that is likely to affect its value. Are
these expectations consistent with our model's views and if not can we argue against
them?
Similarly when doing a comparison against past values of the company we must
determine if enough has changed in the economic prospects to merit the price change. If
their has been no price change for much time then we must determine if our estimated
price is consistent with the market price, and if not we must determine if we have a good
reason to defend our view of the value of the company. It is important to remember that
comparison with market values does not give the answer of whether we have properly
modeled the company or not, just like comparison with an NPV model does not. We
engaged in real options valuation because we thought that both could be wrong. But it
does add some rigor since we will be forced to defend our view against another
alternative.
4.5.3 In Case of Discrepancies Look at the Following
If by any of the review methods above or other insights we recognize that the
result of the process does not seem to assign the correct value to the company, then we
should try to locate the error that lead to the problem. This may involve more than one
issue and if it is the case it will take more than one correction for the model to give the
right value. We should go about it by tackling the more suspect issues first, one at a time,
in order to see which are the minimal corrections that give the result that is closest to the
intended. Then we may correct a few issues at a time and stop when we believe we have
achieved the best model and it is proved by a value we consider appropriate.
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4.5.3.1 Check for double and under accounting.
The first step in locating a potential error is merely checking if the books balance.
In particular we want to make sure that the cash inflows and outflows that the company
reported for the current and past periods add up to their reported values. To do this we
must remember to include all the information we have built into our model when doing
the addition. Broadly speaking the company should have the exact -or at least the
approximate- net cash flow for the periods we are studying as reported on financial
statements. Nevertheless we must remember that when doing our real options modeling
the emphasis is on company insight, and not necessarily on accounting accuracy, and
therefore we can not be too stringent with this requirement.
Should we find any discrepancy there are at least two fundamental reasons why
they may have arisen. One is that we did not incorporate certain items that we should
have. Another is that we could have incorporated certain items twice, by assigning them
to different projects. In either case the model has to be redesigned, and care should be
taken of quick fixes that may result in an economically faulty setup.
4.5.3.2 Has any project been overlooked or confused?
Another potential source of errors is overlooking certain lines of business in the
company, especially if they are small or uncertain yet, and are therefore not clearly
visible to valuators. Just as likely is that a project that may have been valued as a cash
flow might really be an option, or vice versa. For example a company's research lab may
be secret and it may contain very valuable ideas that the market as a whole knows about
or assumes correctly and that individual valuators are bound to miss. But often the
sources of such errors are not as undercover as the last example suggests and merely are
the result of simplistic or incorrect models.
For example it is conceivable that a valuator trying to arrive at correct market
price for EMC Corp., the storage company, may concentrate on the storage systems
business and overlook the faster growing but somewhat smaller storage management
software business. Both will probably qualify as growth option businesses but the second
is clearly the one that experiences the greater level of cash flow volatility and uncertainty.
That implies that a model that emphasizes the management software part would result in
a greater computed value.
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4.5.3.3 Are the DCF projections and WACC reasonable?
These are questions that are to be asked of any DCF model. In case of valuation
problems we first ask if our cash flow projections are reasonable, and then we ask if the
cost of capital we have used to discount them is realistic. Of these two often the discount
rate is the more controversial issue, though many valuators hotly debate each others' cash
flow projections. The issue with the discount rate is that some valuators, such as venture
capitalists, are prone to exceedingly high rates in order to compensate the bias that the
other side -often the entrepreneurs who produced the cash flow forecasts- themselves
introduce. In the financial community discount rates used for new economy companies
vary from 12% to 60%. In the long run few people think that 60% is a realistic cost of
capital but it is indeed the case that a privileged few new economy companies -such as
Dell Computer during the 90s- have achieved compounded rates of return in excess of
100%; but these are the exceptions that confirm the rule that over the long run rates of
return much above the long term market average -between 10% and 15% depending on
the starting year and the index used- are unreasonable. Thus use of very high discount
rates will significantly decrease company value when it is less appropriate to do so, since
most uncertain project will have been be valued as options.
On the issue of cash flow projections it is a matter of judgment, but just like in the
case of the discount rate if it is necessary to assume a very high rate of growth then the
project might have been better valued as an option project. Certainly any cash flow that
increases at a rate greater than 30% is better valued as an option, but even so most
traditional old economy companies will not have cash rates of growth greater than 10%.
Thus care must be taken that if the assumed rate of growth is too high, then the project is
more an option than a cash flow. One such example is Gap Stores Inc., a specialty retailer
that for much of its history achieved revenues growth above the 20% mark. Yet much of
this growth came from new stores sales -the exercising of growth options- as old stores
usually achieved rates of growth no larger than 10%. Though the company could well
have been completely valued as a cash flow company, it is clear that its growth came
from the exercising of its options.
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4.5.3.4 Are the option payoffs and asset value accurate?
Just like in valuing cash flow projects estimates could be in error, it is possible
that the assumptions that go into the determination of option project parameters may be
faulty. When this is the case option values will be out of line and thus the company value
will be too. One of the most likely ways this could happen is if the payoffs of the project
have been either under or over estimated. If this is the case we should determine whether
we have properly projected the future value of the underlying cash flow. For example, if
we are estimating the value of Unix server and workstation manufacturer Sun
Microsystems we may wish to know whether we have properly projected the rate of
growth of one of its product lines. If we are trying to project servers and we have
assumed that they grow in revenues -in the upwards path- at 10% a year a look at what is
happening in this market well tell us that we have underestimated the parameter.
Conversely if we assumed 200% growth in the upward path, maybe our views are too
optimistic. The other parts that go into the determination of the payoff are no less
important: these are the various costs associated with the product. An assumption that
Sun enjoys 80% gross margins in servers is unrealistic given that such products are
manufactured goods. If still we have doubts over our payoffs maybe our model is at fault.
An option can well deviate from the standard strike plus fraction type we described
previously and we should be open to such issues.
The other critical parameter in the real options solution process is the present
value of the cash flows. This is not just the cash we can take out from the project today,
but all the cash we derive from it at all periods of time into the future discounted to the
present. For traded equity this is just the price of the stock. For projects of more than one
period that matter is more complicated. In the case of an option of a single branch we
have to discount all the cash flow payoffs at the risk free rate back to the present to arrive
at S. In the case of an option with multiple branches we have to do the same but
weighting the value of each branch by their risk neutral probabilities as determined by the
binomial formulas. We can do this by using the binomial probability formulas given in
the previous chapter. Given the importance of the current value of the asset in option
price determination, care must be exercised with this issue.
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4.5.4 Redesign if necessary but remember the 80/20 rule
It is important to remember if redesigning our model that simplicity is key to
insight. Complicated models will add little information to the picture and will cloud the
sources of value in the company. In many scientific disciplines, including valuation, there
is the well-known rule that we can capture 80% of the realism with only 20% of the
detail. It is at this balance that we seek to arrive.
For example it may be the case that refining the portfolio to include more
individual projects that currently sit rolled up within others will serve to alter the value of
the company by 5%. In the case of new economy companies 5% is too small a valuation
difference to merit the extra hassle. The value of established technology, Internet, and
other new economy companies can typically fall and rise by 5% during a typical trading
day. Higher growth ones with more uncertain futures can easily do so by 10% or more.
Thus this level of detail is not merited if that is the only change we will have. On the
other hand remodeling is sometimes more about understanding than it is about value. If a
systems company has products in the hardware and software sectors it may make sense to
split these two in order to understand better the company, whether the change will result
in an altered value or not. As we have mentioned before this could be the case of EMC
Corp., whose storage management software group is of strategic importance beyond its
cash flow value. But notice that this strategic value can be understood, and in fact is, a
value that is reflected as an option potential.
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5 Two Examples of Valuing Internet Infrastructure
Companies
5.1 Sycamore Networks
5.1.1 Understanding the Optical Networks Company
Sycamore Networks is a manufacturer of software based optical networks
equipment for the network service providers markets. Its hardware and software products
allow their clients to easily meet the demand for high speed data services over their fiber
optic networks by easing transition from old to new technologies, providing scalability,
interoperability and intelligent systems that reduce the costs of deployment, maintenance
and upgrading. In particular Sycamore's products allow network operators to eliminate
certain legacy hardware -such as SONET/SDH equipment- and to avoid altogether the
conversion of optical signals back to electrical signals once they are on the optical
networks for purposes such as routing. In today's environment of rapid change and
progress in the optical data networks markets -that drive the Internet and other data
networks- these products are very valuable.
Sycamore was founded in February 17, 1998 and since it has been developing its
hardware and software products, and building its administrative and sales organizations.
In May 1999, during the last quarter of its first full fiscal year, it begin shipping its first
completed product, the SN 6000 Optical Transport Product, to its first customer:
Williams Communications. In its second full fiscal year the company added eight new
customers, including both US and international network operators such as Storm
Telecommunications Limited, Enron Broadband Services, and 360 Networks Inc. It also
expanded its commercialized products to include the SN 8000 Add/Drop Product, the
16000 Switch, and the SILVX Network Management Software. Moreover the SN 8000
was upgraded during the year to support new requirements and technologies such as
Gigabit Ethernet and the ability to operate 1600 Km without electrical regeneration. The
company also acquired Sirocco Systems during the fourth quarter of fiscal 2000 to add its
network edge optical switching product. The company has added employees, numbering
800 by the end of fiscal 2000, expanding R&D, sales and support, marketing and others.
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It also expanded its manufacturing agreements with Celestica -which covers all current
products- and Jabil Circuit -that covers some products under development.
September 7, 2000.
Acquisition of Sirocco
November 1999.
Launch of SILVX
May 1999.
Launch of SN 6000
February 17, 1998.
R&D commences.
August 1999.
FLaunch of SN 8000
June 2000.
Launch of SN 160001
Figure 5-1: A schematic product-centered evolutionary tree of Sycamore Networks. IPO occurred on
October 27, 1999. This was shortly before the launch of SILVX Manager. Thanks to the IPO and
other financing activities the company had 1.5 billion dollars in cash as of 3 1st of July 2000. From a
customer perspective a single client accounted for 100% and 92% of revenues in each full fiscal year.
The company intends to continue to focus in its current four lines of business
(transport, add/drop, switching and management products), but intends to add solutions to
be able to cover the network end-to-end. In particular the company intends to capitalize
on the service providers desire to achieve better network topologies, higher wave counts,
longer transmission distances, and higher speeds, all with the pure optical equipment the
company supplies. Thus it intends to continue to improve the performance of their current
products. Other elements of their growth strategy include working with their customers to
generate demand for high speed data services, continue to utilize a software based
architecture, buy off the shelf components for their products whenever available, and
continue to outsource their manufacturing. The software-based architecture comes as part
of the effort to supply their customers with just in time solutions. Furthermore the
company intends to capitalize on their industry experience and connections to achieve
their goals. The vision of the company is to be to be the leading supplier of intelligent
optical networks management hardware and software worldwide. The company will
successfully capitalize on this vision if they continue to hold the technological lead and
can successfully acquire and retain new customers.
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5.1.2 Structuring its Product Portfolio
Sycamore has four main product lines. The division of these lines has been
designed so that the company is able to cover all important segments in the optical
networks infrastructure marketplace.
5.1.2.1 The SN 6000
The SN 6000 is the transport product in the company's range of offerings. It
allows its users to work within their existing (old technology) SONET/SDH networks
thus facilitating the migration to the new technologies developed by Sycamore. This is
the company's first introduced product. From May 1999 to July
3 1st
1999 of their first
full fiscal year all $11 million was derived from it and just one customer: Williams
Communications. The COGS for the year where of $8,486 thousands, but that includes
set up fixed costs that would not be repeated in the future. Thus 75% percent of revenue
where gone in costs.
5.1.2.2 The SN 8000
The SN 8000 add/drop product is a complete stand alone optical networks
solution. It can be used in ring or point-to-point configurations and for access, interoffice,
regional or backbone networks. Like the SN 6000 it can be overlaid on existing networks
to ease the migration for customers. This product was already introduced in the 1999
fiscal year but did not count significantly for revenues until the fiscal year 2000.
5.1.2.3 SILVX
SILVX
provides
optical
network
management
capabilities
through the
SILVXSource and the SILVXManager products. SILVXSource is designed to run on the
Sycamore's SN line of appliances while SILVXManager runs on centralized management
server stations. The line simplifies configuration, provisioning and management of
networks by automating many labor-intensive processes with software. SILVX products
are targeted at broadband and virtual private networks markets.
5.1.2.4 SN 16000
The SN 16000 is Sycamore's optical routing offering and potentially one of the
most profitable products of the lineup. The product was introduced in June 2000. The
product provides the end-to-end wavelength switching and routing -up to know
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unavailable by any vendor- that is necessary to cost effectively build the mesh topologies
present in today's networks with older technology.
5.1.3 Understanding where its value comes from
We choose to model Sycamore Networks using a real options structure that is
inspired in traditional DCF analysis. We use a five period compound option that assumes
that the company tends to follow an upward path to profitability and therefore presumes
we need only to focus on that path. Lower branches in the tree -which represent decreases
in revenues from the previous quarter- terminate rather than branching further, as it
would be the case if the company where to exit the business after the given period. This
serves us a reminder that the life of Internet infrastructure companies at this early stage is
precarious, and allows us to simplify the model.
S,
S3
ES
7
S2
S4
S6
S8
S8
S
sio
Figure 5-2: Schematic of the event and decision trees used to value Sycamore Networks. The first
period corresponds to end of the year 2000 -where we presumably stand. Projections are done for
full fiscal years 2001, 2002, 2003, 2004 and 2005.
In the upper path we assume a rate of growth of 200%, 150%, 100%, 75% and
50% for the underlying revenue of Sycamore in each successive year. We believe this is
possible given its current rate of growth, the fact that it substantially has only one
costumer, and that some of its products have not derived revenue yet. This leaves the
company with nearly 8 billion in yearly revenues by 2005. This is a large optimistic
number, given that Cisco Systems' 2000 revenues were of 12 billion dollars and Cisco is
the largest data-networking vendor in the world. Nevertheless it is possible and we will
assume this best-case scenario.
In computing the real options value we used a replicating portfolio consisting of
each years revenues and payoffs. To simplify the calculation we assumed that each years
revenue, payoff and options could be computed independently and discounted back to the
present at the risk free rate, rather than compounding the total value of the company
down to the first option. The implicit assumption is that the company will follow the
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upper path of growth even though at each point it may exit, and therefore that we can
split the company by yearly projects rather than by product-line projects. One
consequence is that we can compare the value of the company year wise with the DCF
value. Another is that should the company fail to follow the upper path we know that all
successive years growth and their values will be cut out of the market price and
substituted by the worth of whatever other unknown branch it follows.
12,000,000-Z
10,000,000
8,000,000 .
0 Terminal
20.0.5
U 2005
0"2004
6,000,000-.......02
0 2003
3
02001
4,000,000
2,000,000-
0-2,000,000
Real Options Value
DCF Value
Figure 5-3: Value that is derived from each year in the company's model according to the DCF and
real option models. Notice that in the real options model more value is given to the future growth
opportunities than in the DCF model. Also notice that in the DCF model there is some negative value
assigned to the first period due to heavy investments relative to payoff.
We have further assumed that the company gets more efficient in its operations
and investments as it matures, therefore expending less as a fraction of revenues in
COGS, R&D, sales and marketing, and property. We have based the forecast of these
expenses on industry standards -as determined by Cisco Systems and other Internet
infrastructure companies- while remembering that Sycamore is a company with certain
strategic traits such as strong commitments to research and outsourced manufacturing.
The trade off between such forces -as high R&D investment and low manufacturing
expenses- determine its free cash flow. We have assumed away corrections due to
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changes in working asset and liabilities. Also for simplicity and given that it is almost
entirely true we have assumed the company has no meaningful debt.
Our real options model gives us a value of over $10 billion for Sycamore
Networks given our company assumptions and a risk free rate of 5%. By contrast the
DCF model we computed gives us a value of $6 billion when using a cost of capital of
17% (this number was determined following the example of Morgan Stanley's Internet
equity research group). One thing that is important to understand is that these models are
highly sensitive to the assumptions made. Increasing revenues forecast by several dozen
percent each year and decreasing the operating expenses and investments of the company
by 5% of revenue increased value in the real options model up to $15 billion. Clearly
those are the two parts of the model that are driving value. Should the company be able to
gain new customers and diversify by means of R&D and acquisitions fast enough it will
be able to be demonstrate the $8 billion worth that the market is currently assigning it.
Given that in 2000 its value peaked at $50 billion it would seem to be a bargain.
Nevertheless we are inclined to believe it is closer to fair price now given our
assumptions and therefore would issue a cautious buy at $8 billions or less in market
value (approximately a price of $30 a share or lower).
5.1.4 Reviewing the Model
In our model we have made many simplifying assumptions in order to be able to
have an intuitive picture of the company. It would be more economically correct to draw
a more exhaustive event tree that would include more possible states of the world,
including both more optimistic and pessimistic scenarios. At this stage Sycamore is a
company that experiences great volatility in its revenue base and as such could be worth
more than what our current model suggests. Nevertheless such a model would require
however a way to automate the determination of management decisions (ie investments)
at each point in time to make it tractable, or alternatively it could simplify the decisions
from complex accounting based ones to simpler financial options inspired ones. Another
issue with the model is that the terminal value of the company weights heavily and it is
the most uncertain of parameters. A change in the year six value of the terminal cash flow
by a billion impacts the company worth by almost half a billion. Under this conditions
estimated value could be held hostage by the terminal value.
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$12,000,000
*
$10,000,000
$8,000,000
$6,000,000
-
$4,000,000
-
$2,000,000
Discounted Cash Flow Value
Real Options Value
Market Value:
Figure 5-4: Relative DCF, real options and market values of Sycamore Networks in thousand of
dollars. Assumptions of the model include a 17% WACC and 5% risk free rate. If we believe in our
real options model, then Sycamore is currently undervalued and therefore a buy. Nevertheless strong
growth assumptions went into said model and therefore caution is recommended.
We have already compared the company's DCF, option and market value and said
that our real options value seems reasonable in that light and seems to indicate a positive
investment opportunity. This seems to confirm the reasonableness of our computations.
Nevertheless one key assumption that may improve the result if removed is that each
option can be valued almost independently, sparing us from having to discount the
present value of the company's revenues back to the present to determine a single S.
Having to discount S using DCF techniques would in some ways defeat the point of the
real options process: avoiding the pitfalls of DCF. But nevertheless in some
circumstances it may necessary to seek support in the technique. DCF can not be entirely
avoided and even in a real options context it must be used as part of the model.
5.2 Check Point Software Technologies Inc.
5.2.1 Understanding the Security Software Company
Check Point Software Technologies is the worldwide leader in security software
for the Internet and private networks. Its main two product lines, Firewall-1 and VPN-1,
allow companies, governments and institutions to have presence in the Internet and other
networks while reducing the risks of intrusion, snooping and other security breaches that
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are generally made easier by network connections. The company also develops and
markets network software that provide performance and availability services, such their
leading FloodGate-I bandwidth management solution, and network management, such as
Provider-1 and Meta IP. The companies success rests on its Stateful Inspection network
security technology standard, which allows users to experience greater performance,
scalability and the ability to add new applications much more efficiently than with older
architectures. It also has leading technology in network queuing, and IP address mapping.
All of these products are immensely valuable in the Internet economy, where ecommerce, supply chain management, and other network application increasingly require
greater, but more secure network connections with other parties and the outside world.
Check Point Software Technologies was established in Israel in 1993. Its first
product was the Firewall-1, which was introduced in April 1994, and for which revenues
where recognized in the third fiscal quarter of 1994. Since, the company has expanded
the Firewall-1 family of products and added the VPN-1 family. Most of its $425 million
in revenues still derives from its two main product lines. Most of its original revenue
generated from corporate clients but the service provider market has experienced faster
growth and may thus make most of the revenues in the future.
The company intends to continue its strategy of being the leader in network
security software by pursuing four main strategies. It intends to remain an easy supplier
of software and hardware product, by keeping simple its product offerings and
distribution methods and pricing schedules. It intends to aid the establishment of the
Open Platform for Security (OPSEC) standard established by the company in 1996.
Check Point also intends to extend its comprehensive end-to-end security solutions
portfolio to cover all elements of the network. Finally they intend to further their sales
reach, as they have done by expanding in Europe, Latin America and Asia. Check Point's
Strategy is thus primarily to stay focused in retaining and expanding its market leader
role in security for the Internet. In this role it competes against many Internet related
companies, including some much larger corporations such as Cisco Systems, but Check
Point's superior products and range of offerings should allow them to keep the lead.
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5.2.2 Structuring its Product Portfolio
5.2.2.1 Security
Firewall-I is a security suite that integrates access control, authentication,
encryption, network address translation, content security and auditing. This product line
gives the company 32% of the worldwide firewall market making it the clear leader in the
field. Other than the flagship Firewall-i based on the company's Stateful Inspection
technology, other security products are Firewall-1 SecureServer -a cost effective solution
for single servers running critical applications-, Multigate -which provides enterprises
and service providers point-of-presence based security-, and Check Point RealSecure -a
real time attack recognition and response system. Substantially more than half the
company's revenues have derived from Firewall-I sales.
5.2.2.2 Virtual Private Networks
VPN-1 allows companies, their customers, suppliers and other related parties to
establish their own secure virtual private networks (VPN), distinct from the Internet,
while protecting their resources and information in a similar way to that done on Internet
with Firewall-1. The entire line includes VPN-1 Appliance Family, VPN-1 Gateway,
VPN-1 SecureClient, VPN-1 SecuRemote, and VPN-1 SecureServer. The functions of
this line of products include protecting servers, clients, remote connections and other
network parts from eavesdropping, data tampering and other intrusions. Most of the non
Firewall-1 revenues of Check Point derive from the VPN- 1 family.
5.2.2.3 Network Performance and Availability
Performance products include FloodGate-1, which provides convenient data
traffic management to avoid congestion on Internet and Intranet links. ConnectControl
enables other Check Point Software to balance the connection load among several
available servers. VPN-1 Accelerator Card is a hardware based product that improves
VPN performance by accelerating encryption.
5.2.2.4 Network Management
The company also includes several network management solutions that facilitate
the task of administrators in monitoring, assigning, and upgrading system resources.
Provider-i allows (Internet and other) service providers and large enterprises to centrally
5-78
monitor and assign security policies or corporate sites while providing isolation between
customer databases. Meta IP allows automated IP addressing and naming. It uses Check
Point proprietary User-to-Address Mapping (UAM) technology. Other management
software produced by the company includes Account Management Module, Open
Security Extension, Reporting Module, and VPN-1 Certificate Manager.
5.2.3 Understanding where its value comes from
For Check Point we used the same tree structure we used for Sycamore Networks,
but updated the parameters to match the software company. The table that describes
Check Point's valuation process is at the back in the appendix. One of the key advantages
of Check Point is that the company enjoys a very low cost structure. Part of this comes
from being a software rather than hardware manufacturer, which decreases the variable
costs of the company. While Sycamore was constrained to variable costs of between 55%
and 30% of revenues (at 50% representing ownership of only half an option), Check
Point had gross margins of up to 92% or variable costs of just 8%. In the bottom line its
margins are of around 50% after expenses, which consist mostly of sales and R&D.
1c0,000120,000-[
100,000-
,
80,0006000-
hc Proit bsnsien
bt
cs freeuso
n 5-:Rltiegosprft
Figure~~~~~~~~~~~~~~~~~~
frtegv
of
ecbarpesnstaRevenues
The total height
dollars.
thousand
of in
Sycamore
0
Sycamore (2000)
Check Point Products (1999)
Check Point Services (1999)
Figure 5-5: Relative gross profits and cost of revenues of both Check Point business lines and
Sycamore in thousand of dollars. The total height of each bar represents total revenues for the give
company in the given year.
5-79
In fact one of the more rapidly expanding business segments of the company is its
services group which due to personnel costs has a higher cost of revenue than software
manufacturing. Nevertheless this group still accounts for the smaller part of its revenues
and as such for simplicity and lack of precise segment data we have joined it together
with the product segment as a whole. Having been founded in 1994 Check Point is a
midsize and maturing software firm. As such we have projected slower revenues growth
than for Sycamore. Its sequential year-to-year growth on the upper path of the tree should
be 100%, 90%, 80%, 75% and 70% in each of 2001 through 2005. On the lower branches
we have also assumed it is less likely to loose revenue by only allowing falls of 10%, 8%,
5%, 3%, and 2%. This assumptions are justified on the basis that the need for security
solutions is sure to grow as VPN's and e-commerce applications gain prominence, that
Check Point is the established leader in security software for the Internet, and that in
particular it already commands a substantial share of the firewall market.
18,000,00016,000,
0
14,000,000M Terminal
M2005
12,000,000-J
L2004
. .2.003
10,000,000-
12003
S2002
8,000,000-
M2001
6,000,0004,000,0002,000,0000Real Options Value
DCF Value
Figure 5-6: Value that is derived from each year in the company's model in thousands of dollars
according to the DCF and real option models. Notice that in the real options model more value is
given to the future growth opportunities than in the DCF model.
With the assumptions described above the real option value of the company is
approximately $17 billion. This compares with a DCF value of $13.5 billion. Like with
Sycamore much of its value is weighted towards later years. We believe the company
will continue to perform well, but in one particular line it will loose some of its financial
5-80
appeal. The company currently enjoys a tax break from the government of Israel designed
to encourage high tech companies to establish themselves in the country. That translates
into the company having an effective tax rate of between 3% and 6%, mostly due to the
tax liabilities of its American subsidiary. With the expiry of the last elements of the break
by 2005 the cash flow the company generates will decrease. Because of all the reasons
above we do not recommend to buy, though current owners of the shares should hold. We
would buy at market caps of $15 billion or below.
5.2.4 Reviewing the Model
In studying whether our model successfully describes the value of the firm we go
back to the financial markets for guidance. Currently being worth more than $20 billion
the company seems to be overvalued in the markets or undervalue by our model. Given
the already optimistic assumptions in the model we are inclined to believe it is
overvalued in the markets.
$25,000,000-
$20,000,000
$15,000,000
$10,000,000 -
$5,000,000 -
Discounted Cash Flow Value
Real Options Value
Market Value:
Figure 5-7: Check Point Software's DCF, real option and market values in thousands. Model
assumptions include a 17% WACC and a 5% risk free rate. The data seems to suggest that Check
Point Software is currently overvalued but given the price volatility of the stock it is very close to fair
value.
To support this view we notice that Check Point, unlike Sycamore, is currently
trading close to all time highs. The company has not suffered the deep corrections that
other sectors in Internet infrastructure have. Only storage leaders such as EMC Corp.
5-81
may be holding their market value better than Check Point. And therefore we believe the
company will either experience a correction or have zero returns for the foreseeable
future.
Changes that could be done on the model to improve its insight is to split the
company into its product and service operations. The product operation will still
command higher multiples, but higher growth at services, which could equal products in
several years, may serve to explain a higher value. On the down side the phasing out of
the tax breaks may work to reduce the cash flow available to the company. Factoring
other liabilities such as accrued severance payments (required by Israeli law) will further
reduce the value of the company. Also like in the case of Sycamore much of the value is
assigned to the terminal year, which may need refinement. Currently it is assumed to be a
multiple of the previous year revenue or cash flow, but a growing annuity followed by a
slower growing perpetuity might be more realistic.
5-82
6 Conclusion and a Look into the Future
In this paper we have discussed some, but by no means all, of the most important
issues in applying real options theory from both a theoretical and practical point of view
to valuing and understanding new economy companies. As is fundamental to any option
problem we have discussed the importance, value and impact of future uncertainty and
managerial flexibility in dealing with it. Because of that it becomes even more evident
that managerial skill is of fundamental value in technology and other high growth
companies. A manager that does not know how to envision and prepare for the future will
miss many golden opportunities that his rivals will surely take. It is in fact probably
because of this that so many companies exist in new industries, so that the chances that
some will achieve the goal are increased. It would be very interesting to pursue this line
of study further to develop an understanding of how much value does a manager truly
bring to a company, whether that has to do with the uncertainty he encounters and the
flexibility that he must muster, and whether that serves to justify some of the more
extreme compensation packages among new economy firms.
A point of more practical than theoretical interest is to extensively study
compound binomial real options. These, in essence, are the workhorses of company real
options valuation and as such a good understanding and a developed framework can
make a large difference between meaningful results and none. Compound options are
fundamental to companies because everything a company does has impact on the future
opportunities that will be available to it. They also provide the practical bridge necessary
to unite DCF valuation and strategy, as they allow following courses of action or
evolution and measuring the impact they have on company value. Until a few complex
systems of binomial compound options have been understood and thrown into userfriendly frameworks universal application of real option theory will remain limited to a
few practitioners. Another area of real options theory that will require further study in
order to truly allow practical use of the theory is how to numerically and yet intuitively
deal portfolios of options, especially compound options as described above.
Visualization has important applications in real options and any sort of company
analysis. By means of visual diagrams we are able to understand and communicate better
what are the important characteristics of the company under question. By means of visual
6-83
diagrams we can study the evolution of companies, their product markets, their customer
markets, and their future plans. We can also grasp better what is their worth and how is
their value dependent on the outcome of future events. Financial markets value
companies based on the available
information and valuators
assumptions
and
expectations. As such, changes in expectations and assumptions can cause large changes
in the prices of companies' equity and understanding the risk in this is an important use
visualization. Thus visualization can and should be extended to be able to grasp at a
glance how much are companies worth, and how much would they be worth if our model
assumptions changed instantaneously.
In the end, all of what we have mentioned above are tools or ideas. What we
really want the most is to put them to practical use. One such potential use, just as I have
intended to illustrate by example, is in equity research and valuation as done by financial
analysts. In terms of absolute output to society it is just as valuable that more analysts
should learn and use real options techniques than it is that researchers continue to develop
the theory in all its mathematical grandeur. If real options where better known by
practitioners it would come less as a surprise the seemingly irrational market behaviors
that have characterized the recent past, less money would be lost, and more profits would
be made. The investment management community will be better able to grasp the value
of technology companies, and they would be able to deliver better results to investors in a
less volatile market place. In a way this paper was a marketing campaign on the
democratization of real options, but more work remains to be done.
The other area where real options theory has the greatest potential is in
entrepreneurship. Real options bridges the divide between the unknown and value, and in
the process allows us to better grasp the principles of entrepreneurship and innovation.
Value is created when uncertainties are resolved. Aspiring entrepreneurs and innovators
and their financial backers now have the tools to tackle their planning and decision
process. But just like in the investment community more democratization of the theory
has to be done in R&D labs, startup ventures, venture capital firms and other
entrepreneurial organizations. Innovation is the precursor of wealth and through real
options we can think better about how to innovate.
6-84
7 Appendices
7-85
Sycamore Networks' Real Options Value
1499
11,$00
ibm.
S
Fistl years endS July 31st
200
20)l
20)2
23
2004
2005
198,000
594,0(0,
200%
118,800
-40%
1,485,000
150%
415,800
-30%
2,970,000
$;197,500
7,796,250
100%
1,188,000
-20%
75%
50%
2,524,500
4,677,750
-10%
668,250
45%
Growth Raftq
!9
Growth Ra
-15%
Tprminap
"Up" Payoff
Fixed C(ost
variable Cost
Percent of ;
8,400
105,000
297,000
74%
5%
50%
Gross Profit
Percent Magin
21900
26%
93,000
41%
297,000
50%
816,750
1,188,000
40%
1,782,000
1,819,125
35%
$,378,375
55%
60-%
65%
2,338,875
30%
6,457,376
70%
40%
475,200
35%
883,575
30%
1,403,325
564,300
883,5V75
17%
779,625
155,925
3%
1 819,125
35%
70%
1,169,435
15%
1,169,436
15%
233,885
3%
2,572,763
33%
63%
259,875,
5%
2 079,0(0*
389,81.
5%
2,962,567
lDow " Payoff
Variable Cost Percen# of S
50%
45%
59,400
187,110
148,SpO
25%
89,100
15%
17,6t20
3%
255,4o20
43%
93%
326,700
22%
222,750
15%
44,550
3%
594,000
40%
85%
41,000
21%
131,700
89,100
15%
344,51O
148,500
10%
742,500
-38,700
-47,420
-40,615
74,250
54,241
534,600
333,786
299,3'5
693,412
98,25
340,350
954,169
2,052,4$3
Gross Profit
Invest;nts'
Research & Daveloprpent
Percent of S)
Sales aind Mat*eting
Percent of $
Generg and Administrative
Percent of $
Total Value of Operating InVoystments
Percent of $
Tota/ Perceat of Operating Expenes
Purchases of PropefrY,
Percent of $
14,00
124%
4,900
35%
1,400
12%
19,400
172%
246%
Plant & Equip.
51700
50%
25,100
Total Viue af invesonents
Net "p" Cash Flow (PayofFInveQnert
Present valu discoontedt:
Discowsed Cash Row Vahwe
'Vlue of eacA years',C' dlscountedat:
Real Options Value
17%
$
54.00
2o%
30,000
li%
6,700
3%
90,700
40%
90%
1,$%
445,500
16%
89,100
$%
1,098,900
37%
77%
148,500
$%
1,247,400
1%
2,494,800 16o0,001
1,137,900
3,098,38$
3,551,447
3,98,380
4,077,117
5%
$ 10895,041
Ma*et# Vbke:
$ !,000,Q0, As Uf February 2, 401
Check Point Software Technologies' Real Options Value
Items
5,
1998
219,000
2rO0
425,000
Growth Rate
Sd
Growth Rate
Fiscal years ends December 31st
2003
2Q04
5,087,250
2005
ermisI
2001
850,000
100%
382,500
-10%
2002
1,615,000
90%
782,000
-8%
2,907,000
40%
1,534,250
68,000
8%
782,000
920/
129,200
8%
1,485,800
92%
232,560
8%
2,674,440
92%
4,680,270
02%
50%
191,250
45%
351,900
40%
613,700
986,927
85,000
10%
212,500
25%
34,000
4%
331,500
39%
47%
161,500
10%
403,750
25%
64,600
4%
629,850
39%
47%
290,700
10%
5811,400
20%
87;210
3%
959,310
33%
41%
508,725
100/
1,017,450
152,018
3%
1,678,793
33%
41%
864,833
10%
1,72905
20%
259X0
3%
2:,853,947
33%
41%
25,500
87,210
3%
357,0001
48,450
3%
678,300
1i,046,520
152, 18
3%
1,831,410
259,460
3%
3,113,397
425,000
363,248;
807,500
589,890
1,627,920
11,016,425
2,848,860
1,520,294
4,843,02
2,208,975
20,000,000
7,796,772
291,972
611,933
li,277,558
2,527,976
4,765,020
7,796,772
~5%
75%
2,819,790
-3%
8,648,;25
70%
4,985,605
-2%
"Up" Payoff
Fixed Cost
Variable Cost
Percent of $
Gross Profit
Percent MWrgin
"Qowun'
22,000
10%
197.000
90%
35,000
8%
390,000
92%
406,$80
8%
691,868
8%
7,956,469
92%
Payoff
Variable Cost Percent of S
Gross Profit
35%
30%
1,495,052
investments
20,000
9%
70,00
32%
13,000
30,000
7%
110,000
20%
20,000
Reserch & 0oveloprment
Percent of S
Sales and Marketing
Percent of S
General and Administrative
Percent of S
Total Value of Operating InVestmeits
Percent of S
Total Percent of Operating Expenses
0%
5%
103,000
47%
57%
160,000
38%
46%
Purchases of Property, Plant & Equip.
Percent of S
Total Value oflnvestmento
6,000
3%
109,000
41,000
10%
201,000
Net ''ilp"Case, Flow (Payo.-nve
Present value discountedat:
Discounted Cash Row Vake
Value pf each year' C' u4',g:
Real
Lpdon& value
189,000
.
$
17%
13,495,04
5%
$ i,271,231
3%,
Market Value:
2W%
$ 22,000,000 As of February 2, 2001
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